{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 一元线性回归\n",
    "\n",
    "生成数据，我们可以适当给数据增加一些扰动来检验线性回归的性能"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def true_fun(X):\n",
    "    return 1.5*X + 0.2\n",
    "\n",
    "np.random.seed(0) # 随机种子\n",
    "n_samples = 30\n",
    "'''生成随机数据作为训练集'''\n",
    "X_train = np.sort(np.random.rand(n_samples)) \n",
    "y_train = (true_fun(X_train) + np.random.randn(n_samples) * 0.05).reshape(n_samples,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "实际模型会存在一个偏置量$b$，以一元为例，$y=w_1x_1+b=w^Tb=w_1x_1+w_0x_0$, 实际使用梯度下降法时可以添加一维并令$x_0=1$,则求出的$w_0=b$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 添加一维数据\n",
    "data_X = [] \n",
    "for x in X_train:\n",
    "    data_X.append([1,x])\n",
    "data_X = np.array((data_X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 梯度下降训练\n",
    "\n",
    "### 梯度下降法的过程\n",
    "<div style=\"text-align: center\">\n",
    "<img src=\"./BGD.png\" class=\"aligncenter\" width=\"40%\">\n",
    "</div>\n",
    "\n",
    "### 如何求取梯度？\n",
    "\n",
    "假设给定模型$h(\\theta)=\\sum_{j=0}^{n} \\theta_{j} x_{j}$以及目标函数(损失函数):$J(\\theta)=\\frac{1}{m} \\sum_{i=0}^{m}\\left(h_{\\theta}\\left(x^{i}\\right)-y^{i}\\right)^{2}$, 其中$m$表示数据的量，我们目标是为了$J(\\theta)$尽可能小，所以这里加上$\\frac{1}{2}$为了后面的简化，即$J(\\theta)=\\frac{1}{2m} \\sum_{i=0}^{m}\\left(y^{i}-h_{\\theta}\\left(x^{i}\\right)\\right)^{2}$。  \n",
    "那么梯度则为：\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\frac{\\partial J(\\theta)}{\\partial \\theta_{j}} &=\\frac{1}{m} \\sum_{i=0}^{m}\\left(y^{i}-h_{\\theta}\\left(x^{i}\\right)\\right) \\frac{\\partial}{\\partial \\theta_{j}}\\left(y^{i}-h_{\\theta}\\left(x^{i}\\right)\\right) \\\\\n",
    "&=-\\frac{1}{m} \\sum_{i=0}^{m}\\left(y^{i}-h_{\\theta}\\left(x^{i}\\right)\\right) \\frac{\\partial}{\\partial \\theta_{j}}\\left(\\sum_{j=0}^{n} \\theta_{j} x_{j}^{i}-y^{i}\\right) \\\\\n",
    "&=-\\frac{1}{m} \\sum_{i=0}^{m}\\left(y^{i}-h_{\\theta}\\left(x^{i}\\right)\\right) x_{j}^{i}\\\\\n",
    "&=\\frac{1}{m} \\sum_{i=0}^{m}\\left(h_{\\theta}(x^{i})-y^{i})\\right) x_{j}^{i}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "设$x$是(m,n)维的矩阵，$y$是(m,1)维度的矩阵，$h_{\\theta}$是预测的值，维度与$y$相同，那么梯度用矩阵表示如下:\n",
    "$$\n",
    "\\frac{\\partial J(\\theta)}{\\partial \\theta_{j}} = \\frac{1}{m}x^{T}(h_{\\theta}-y)\n",
    "$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "输出参数w: [1.445439]\n",
      "输出参数:b [0.22683262]\n"
     ]
    }
   ],
   "source": [
    "m,p = np.shape(data_X) # m, 数据量 p: 特征数\n",
    "max_iter = 1000 # 迭代数\n",
    "weights = np.ones((p,1))  \n",
    "alpha = 0.1 # 学习率\n",
    "for i in range(0,max_iter):\n",
    "    error = np.dot(data_X,weights)- y_train\n",
    "    gradient = data_X.transpose().dot(error)/m\n",
    "    weights = weights - alpha * gradient\n",
    "print(\"输出参数w:\",weights[1:][0]) # 输出模型参数w\n",
    "print(\"输出参数:b\",weights[0]) # 输出参数b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_test = np.linspace(0, 1, 100)\n",
    "plt.plot(X_test, X_test*weights[1][0]+weights[0][0], label=\"Model\") \n",
    "plt.plot(X_test, true_fun(X_test), label=\"True function\")\n",
    "plt.scatter(X_train,y_train) # 画出训练集的点\n",
    "plt.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scikit-learn\n",
    "scikit-learn，简称sklearn，是一个开源的基于python语言的机器学习工具包。它通过NumPy, SciPy和Matplotlib等python数值计算的库实现高效的算法应用，并且涵盖了几乎所有主流机器学习算法。\n",
    "\n",
    "官网：https://scikit-learn.org/stable/index.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "输出参数w: [[1.4474774]]\n",
      "输出参数:b [0.22557542]\n"
     ]
    },
    {
     "data": {
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       "<Figure size 640x480 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression # 导入线性回归模型\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def true_fun(X):\n",
    "    return 1.5*X + 0.2\n",
    "\n",
    "np.random.seed(0) # 随机种子\n",
    "n_samples = 30\n",
    "'''生成随机数据作为训练集'''\n",
    "X_train = np.sort(np.random.rand(n_samples)) \n",
    "y_train = (true_fun(X_train) + np.random.randn(n_samples) * 0.05).reshape(n_samples,1)\n",
    "\n",
    "model = LinearRegression() # 定义模型\n",
    "model.fit(X_train[:,np.newaxis], y_train) # 训练模型\n",
    "\n",
    "print(\"输出参数w:\",model.coef_) # 输出模型参数w\n",
    "print(\"输出参数:b\",model.intercept_) # 输出参数b\n",
    "\n",
    "X_test = np.linspace(0, 1, 100)\n",
    "plt.plot(X_test, model.predict(X_test[:, np.newaxis]), label=\"Model\")\n",
    "plt.plot(X_test, true_fun(X_test), label=\"True function\")\n",
    "plt.scatter(X_train,y_train) # 画出训练集的点\n",
    "plt.legend(loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 多元线性回归\n",
    "\n",
    "以三元为例，$y=w_1x_1+w_2x_2+w_3x_3+b=w^Tb$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "输出参数w: [[0. 2. 3.]]\n",
      "输出参数b: [1.]\n",
      "预测结果: [[22.]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "X_train = [[1,1,1],[1,1,2],[1,2,1]]\n",
    "y_train = [[6],[9],[8]]\n",
    " \n",
    "model = LinearRegression()\n",
    "model.fit(X_train, y_train)\n",
    "print(\"输出参数w:\",model.coef_) # 输出参数w1,w2,w3\n",
    "print(\"输出参数b:\",model.intercept_) # 输出参数b\n",
    "test_X = [[1,3,5]]\n",
    "pred_y = model.predict(test_X)\n",
    "print(\"预测结果:\",pred_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 多项式回归以及过拟合与欠拟合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### 训练集\n",
    "用来训练模型内参数的数据集\n",
    "\n",
    "### 验证集\n",
    "用于在训练过程中检验模型的状态，收敛情况，通常用于调整超参数，根据几组模型验证集上的表现决定哪组超参数拥有最好的性能。\n",
    "\n",
    "同时验证集在训练过程中还可以用来监控模型是否发生过拟合，一般来说验证集表现稳定后，若继续训练，训练集表现还会继续上升，但是验证集会出现不升反降的情况，这样一般就发生了过拟合。所以验证集也用来判断何时停止训练\n",
    "\n",
    "### 测试集\n",
    "测试集用来评价模型泛化能力，即使用训练集调整了参数，之前模型使用验证集确定了超参数，最后使用一个不同的数据集来检查模型。\n",
    "\n",
    "### 交叉验证\n",
    "\n",
    "交叉验证法的作用就是尝试利用不同的训练集/测试集划分来对模型做多组不同的训练/测试，来应对测试结果过于片面以及训练数据不足的问题。\n",
    "\n",
    "![jupyter](./cross_valid.png)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fp3Pnzrzxxhu4uLgwb948Hn74Yfbu3cs777yT4pjhw4dz9913J9tWuXLlLMV9u1OnTtGiRQv8/f358MMPiY6OZvz48fz7779s3rwZNzc3275vvPEGpUqVol69eixdujTNc9arV4+GDRvyySef8NNPP2VrvFLwKPdnzJYtW2jevDmPPfYYHh4e7Nixg48//pjly5ezZs0anJwsn++MGTOG9evX8+CDD3LXXXdx7tw5Jk6cSP369dm0aRO1atXKtscRHR1N69atiYyM5LXXXsPV1ZXPPvuMli1bsnPnTooWLQrAH3/8wZgxY+jRowePPvooiYmJ/PTTT7Rv354ff/yRxx57LNl5J0yYQIUKFWjdunW2xXr27Fl27NjBu+++a/exr7/+Ok8++WSybdeuXePpp5/O0N+SjObZ6OhoGjduzLVr1xg6dCjBwcHs2rWLiRMnsnLlSrZt22Z7nrMqJ567UqVK0b17d8aPH0+3bt2yJU7JvwpLbl+0aBHff/89d911FxUrVrT7TfTLL7/Mp59+Sv/+/Rk6dCgRERFMnjyZli1bsn79eho1agTY/xo6J2U0f5jNZtq3b8/evXsZOnQoVapU4dChQ3z99dcsXbqUffv24evrazvvuHHjaNu2bba+1t28eTOXLl2iS5cumT7H7b9nzs7Odp/jzTffJCYmJtX7cvPvdnpy4rnNF+8LjEJuypQpBmD07NnTKFasmJGQkJDs/sGDBxsNGjQwQkJCjC5duti2z5492wCMGTNmpDjn9evXjcjISNv3b731lgEYFy9ezLkHYqfz588b/v7+xrvvvmsAxrhx4zJ0XI0aNYw6deok+zm9/vrrhslkMvbt22fbNnjwYMPNzc0IDw9PdnyLFi0MPz+/7HkQN3Tq1MkoXbp0sp/5d999ZwDG0qVLbdtiY2ONs2fPGoZhGFu2bDEAY8qUKamec/v27QZgLF++PN3rt2zZ0nj00UczFOuAAQOMli1bZmjftGTmuTty5Ihx7NixZNvMZrPRpk0bw93d3YiOjrZtX7lypQEYc+bMyVKcGfHMM88Ynp6exvHjx23bli1bZgDG5MmTk+179OhRwzAM4+LFiwZgvPXWW2med/z48Ya3t7dx9erVnAhbCgDlfvtyf2rGjx9vAMbGjRtt29avX2/ExcUl2y8sLMxwd3c3+vXrl+lrpWbMmDEGYGzevNm2bd++fYazs7MxatQo27Y9e/akeA5iY2ONatWqGWXLlk22PT4+3ihWrJjxxhtvpHv9t956ywgJCclQrD/88IPh6elpxMTEZGj/9EyfPj3N38PbZTTPzpgxwwCMhQsXJjv+zTffNABj+/bt2RK7YeTMc2cYhjF37lzDZDIZhw8fzrZYJX8pbLn93Llztrzy7LPPGva8tUtISDA8PT2N3r17J9t+5MgRAzCGDx9u22bPa+isCAkJuePrO8PIeP5Yv369ARgTJ05MdvyPP/5oAMb8+fNt286fP2+4uLgY33//fboxPvrooxl+LT969OgM/524XXb9nv3777+Gi4uL7e/+7a/vc+vvtqOeW8PI++8LCv2UJau+ffsSHh7OsmXLbNvi4+OZO3cujzzySIr9Dx8+DEDTpk1T3Ofh4YGfn1/OBZsNXn31VapWrUr//v0zfMzevXvZu3cvTz31FC4uNwdXDR06FMMwkg2Bi4qKwsPDI8WnBKVLl8bT0zPZNrPZzOeff07NmjXx8PCgZMmSDBkyhCtXrqQbU1RUFMuWLaN///7JfuYDBw7Ex8cn2dQgd3d3SpUqlaHH+vvvv+Pm5kaLFi0ytH9GmM1mlixZkqUqOWTuuatQoQIhISHJtplMJnr06EFcXFyqQwEBrl69mup0tFv9/PPPNGjQAE9PTwIDA3n44Yc5efJkhuKaN28eXbt2pVy5crZt7dq1o0qVKimmdZUvXz5D5wRo3749165dS/b/WSQ1yv2ZZ/0/GRERYdvWpEmTZCPbAEJDQ6lZsyb79u1LcY7FixfTvHlzvL298fX1pUuXLvz3338Zuv7cuXO5++67k43kq1atGm3btk2WP2rWrEmxYsWSHevu7k7nzp05deoUV69etW1ft24dly5dol27dhmKIaP+/PNPWrduneLvX2bNnDkTb29vunfvnu6+Gc2zUVFRAJQsWTLZ8aVLlwZIEXtee+6sjwssI2ukcCssub1kyZKZzisJCQlcv349xf/5EiVK4OTklOy89ryGhqzlh/RkNH/Yk9P+/PNPEhMTcyT3Z/V1v2EYREVFYRhGpo5//vnneeCBB2jevHmq9+fm3+305MRzC3n/fYEKMjeUL1+exo0bM2vWLNu2xYsXExkZycMPP5xif+ub259++inD/0EuX77MpUuXkn3d+kI2LZGRkSmOS+3r9rn8adm8eTPTpk3j888/t2uu6Y4dOwBo2LBhsu1lypShbNmytvvBMuc9KiqKIUOGsG/fPo4fP84333zD/PnzGTVqVLLjhwwZwssvv0zTpk2ZMGECjz32GDNmzKBDhw4kJCTcMaZ///2XxMTEFDG5ublRt27dZDHZY8OGDdSqVSvD8/MzYsuWLVy8eJHOnTtn+hyZfe7SYp3nfPsLXoDHHnsMPz8/PDw8aN26NVu3bk2xzwcffMDAgQMJDQ3l008/ZcSIEfz999+0aNEi3d/t06dPc+HChRTPHUCjRo0y/dwB1KhRA09PT9avX5/pc0jhoNyfcYmJiVy6dIkzZ87w119/8cYbb+Dr62sb0p4WwzA4f/58ijwzffp0unTpgo+PD2PGjGH06NHs3buXZs2acezYsTue02w2s3v37jTzx+HDh1O8Wb/duXPn8PLywsvLy7Ztw4YNmEwm6tWrd8dj7ZGQkMDy5cuzlPtvdfHiRZYtW0aPHj3w9va+47725NkWLVrg5OTE888/z6ZNmzh16hSLFi3igw8+oEePHlSrVs22b1587gD8/f2pVKmScr8UqtyeWZ6entxzzz1MnTqVGTNmcOLECXbv3s2gQYMICAjgqaeeytR5s5If0mNP/mjYsCHe3t6MHj2aFStWcPr0aVavXs0rr7zC3Xffnaz4smHDBooWLZriw8usOHfuHDt27Mhy7q9YsSL+/v74+vrSv39/zp8/n+Fj58yZw4YNG+zuYZMTf7fTk1PPLeSD9wWOG5yTN1iHNm7ZssWYOHGi4evraxv69+CDDxqtW7c2DMNIMbQxJibGqFq1qgEYISEhxqBBg4wffvjBOH/+fIprWIecpfZVtWrVdGNs2bJlmsff+pWRaTNms9lo1KiR0bdvX8MwLNNAyOCw9XHjxhmAceLEiRT33X333ca9995r+z4xMdEYNmyY4erqaovP2dnZmDRpUrLj1q5dm+oQ0SVLlmRoOPacOXMMwFizZk2K+x588EGjVKlSqR6X3nDLsmXLGr169brjta0yOmUpK8MWDSNrz11qwsPDjRIlShjNmzdPtn39+vVGr169jB9++MH4448/jI8++sgoWrSo4eHhkWzI+rFjxwxnZ2fjgw8+SHa8dWjk7dtvZ30OfvrppxT3vfzyywZgxMbGprgvI1OWDMMwqlSpYnTq1OmO+0jhpdxvf/7YuHFjisewcuXKdI+zTq/54YcfbNuuXr1qFClSxBg8eHCyfc+dO2f4+/un2H47ax549913U9z31VdfGYCxf//+NI8/ePCg4eHhYQwYMCDZ9v79+xtFixZN9zEZRsanLP39998GYJt2mVVffvmlARiLFi1Kd1978+z3339vFClSJMXv163TPvLqc2d13333GdWrV79jDFJwFbbcfit7pywZhuX/U/369ZNdt2LFinf8P3in19BZzQ/pTWuxN38sXLjQKF26dLLH16FDhxRTV5o1a2Y0aNDgjrFZZXTKUlanqn7++efGsGHDjBkzZhhz5841nn/+ecPFxcUIDQ1NNoUuLTExMUa5cuVsU33saUmQE3+3HfXcWuXl9wVq6nuLPn36MGLECBYuXEjHjh1ZuHAhX3zxRar7enp68s8///DBBx8we/Zspk6dytSpU3FycmLo0KGMHz8+RcOwefPmpRjymN6nWwCffPJJhqbv3N5sLDVTp07l33//TdFhOyOuX78OkOJxgWU4p3X4GFgaTlWqVIkOHTrw4IMP4uHhwaxZs3juuecoVaoUPXr0ACyVW39/f9q3b8+lS5dsxzdo0AAfHx9WrlyZ6tDSjMZkvd9e4eHhBAQEpNiekJBAZGRkim1xcXHJ4gcIDAxM1gBx0aJFWRq2mJXn7nZms5l+/foRERHBl19+mey+Jk2a0KRJE9v33bp1o3fv3tx1112MGjWKJUuWADB//nzMZjN9+vRJ9thLlSpFaGgoK1euvOMqJek9d9Z9Urs/IwICAlI8JyKpUe7PmBo1arBs2TKuXbvGhg0bWL58ebqf4O7fv59nn32Wxo0b8+ijj9q2L1u2jIiICPr27Zvs/6mzszP33HMPK1euvON5M5o/UhMTE8ODDz6Ip6cnH3/8cbL70sr9QIp8EhMTg9lsTrHd19c3WVyLFi2iRo0adk27vJOZM2dSvHjxDC3LbW+eDQoKolGjRnTu3JmQkBDWrl3LF198QbFixWwrcuXV584qICAgSyMspeAoDLk9q3x9falZsyaNGzembdu2nDt3jo8//pgePXqwdu3aVEdQ34k9+SEuLi7FaDiz2UxMTEyKvGqNw978Ubx4cerVq2dbRWjnzp2MHTuWxx57jDlz5tj2Cw8PJygoKMU5zWYzly9fTrYtLi6OhISEFDH6+/snG1m/aNGiLE1Vff7555N936tXLxo1akS/fv34+uuvefXVV+94/Mcff0xCQoLdKwZmx9/tvPTcWuXl9wUqyNyiePHitGvXjpkzZxITE0NSUhK9e/dOc39/f3/Gjh3L2LFjOX78OH///Tfjx49n4sSJ+Pv78/777yfbv0WLFnYnNrAUJ7JDVFQUo0aN4uWXXyY4ONju460JJS4uLsV9sbGxyRLOxx9/zIQJEzh48KCtM3ifPn1o3bo1zz77LF27dsXFxYWDBw8SGRlJiRIlUr3mhQsXAMvwzlv/E7q5uREYGGhXTPYyUhmyun79+lRX3tiwYQO//PJLsm1Hjx61vQA/d+4c27dvT7bCxuXLl4mPj7d97+npmeaKTll97m733HPPsWTJEn766Sfq1KmT7v6VK1eme/fuzJ8/n6SkJJydnTl48CCGYRAaGprqMdY/StHR0cnetDk7O1O8ePF0nztIOQfUHoZhZMu0Lin4lPszxs/PzzYMuHv37sycOZPu3buzffv2VPPIuXPn6NKlC/7+/sydOzfZyhAHDx4EoE2bNmleCywvvm4vgpcqVSrT+SMpKcm2utzixYtTfcOTWu4Hy+9JRrZPmTKFQYMG2b7/888/uf/++23fp5UTM+LIkSNs3LiRYcOGJevllhZ7fk7r16+na9eubNq0yTZkvEePHvj5+fHOO+/w+OOPU6NGjTz93IFyv9xU0HN7Vll7plhXTrVq164dNWvWZNy4cYwZM8auc2Y0PwDMmjUrxSp3YFntaNy4ccm2WfOyPfnjyJEjtG7dmp9++olevXoBlr9d5cuXZ9CgQSxevJhOnTqluMatTpw4QYUKFVJ9LLfn7ZUrV9KqVSvA8mHtsmXL+Oijj2z3p/Vexh6PPPIIL774IsuXL79jQebYsWOMGzeOr776KtWVwNKSHX+3Ie89t9br5NW/DSrI3OaRRx5h8ODBnDt3jk6dOmV46bqQkBAef/xxHnjgASpWrMiMGTNSJO7Muv2Ne1ru9IYeYPz48cTHx/PQQw/Z5vmdOnUKgCtXrnDs2DHKlCmTorGTlbVR0tmzZ1O8qD979myyPgJff/01bdq0SZEEunXrxv/93/9x7NgxKleujNlspkSJEsyYMSPVa1qT3fPPP8+0adNs21u2bMmqVauSxXS7s2fPZvrThaJFi6b66UWdOnVSNIR68cUXKVWqFC+//HKy7bc2P1u8eLGtF4tVz549Wb16te37Rx99lKlTp6YaT1afu1u98847fP3113z88ccMGDAg3f2tgoODiY+P59q1a/j5+WE2mzGZTCxevDjVJfisz/348eOTLasdEhLCsWPH0n3uAgMDMz06Biw/l7SKRSK3U+7PWP64Vc+ePRkwYAC//PJLioJMZGQknTp1IiIigrVr16bIxWazGbDMR0+tUaS12PDrr7+meFFnGIYtP6SVPyD1T5cHDx7MwoULmTFjRqovKtPK/UCK3P/TTz/x119/8fPPPyfbXrNmTdvto0ePsn//fiZNmmTbllZOzIiZM2cC0K9fvwztb0+enTx5MiVLlkwxf79bt268/fbbbNiwgRo1auTZ587qypUrmXqTLAVTQc7tWbVmzRr27NnDp59+mmx7aGgo1atXz1S/jYzmB4AOHTqkyKv9+/fnvvvuY+DAgame3578MXXqVGJjY+natWuy/bp16wZYitDWN+1p5f5SpUqliHHcuHGcO3eOTz75JNn2W/8Orlu3jqioqGT9Y9J6L2Ov4ODgFKN2bvfmm28SFBREq1atbH9frH0jL168yLFjxyhXrlyykfzZ9Xcb8tZza5WX3xeoIHObBx54gCFDhrBp0yZ+/fVXu48PCAigUqVK7NmzJ9tiuv2Ne1ru9IYeLFXeK1euJHuxaPXhhx/y4YcfsmPHDurWrZvq8dbtW7duTVZ8OXPmDKdOnUrW/Ov8+fMkJSWlOIe1Sa915Z5KlSqxfPlymjZtesfREK+88kqyVUGsQ8pr1aqFi4sLW7dupU+fPrb74+Pj2blzZ7Jt9qhWrRpHjx5NsT0gICBFo6iAgABKly59x87sqa2wcfuQ1TsVj7L63Fl99dVXvP3224wYMYKRI0fecd/bHTlyBA8PD1uhpVKlShiGQYUKFahSpUqaxw0cOJBmzZrZvrf+DIKCgihevHiqzYI3b96c7mO5k8TERE6ePGlLzCLpUe5PP3/cLi4uDrPZnGIURGxsLPfffz9hYWEsX76cGjVqpDi2UqVKgGU1jzvlztRe1AE4OTlRu3btVPPHP//8Q8WKFfH19U22/eWXX2bKlCl8/vnn9O3bN9XrVatWjRkzZhAZGZnijdDtca5btw4PD490c7+/v3+yHJhWTsyImTNnUqlSJe69994M7W9PnrXn7zbkvefO6ujRoxka+SmFQ0HO7VllbQ6b1v/79FbZTE1G8wNYCsbWorGVh4cHFStWTPNYe/LH+fPnMQwjxeO7PaeBJffPmzcvxTlTy/E///wzcXFx6eb+26eqpvVexh6GYXDs2LF0G8+fOHGCQ4cOUbFixRT3DR06FLAUKKwFyuz8uw1567m1fp+X3xeoIHMbHx8fJk2axLFjx5INMb7drl27CAoKSvEpzPHjx9m7dy9Vq1bNtpiya67p8OHDbb1brC5cuMCQIUMYNGgQ3bt3tw3LS0hI4PDhw/j7+9v+Q9WsWZNq1arx7bffMmTIENuoiEmTJmEymZINA61SpQrLli0jPDycokWLApaEP3v2bHx9fW3/qfv06cPXX3/Ne++9x4cffpgstsTERKKjoylSpAg1atRINTn4+/vTrl07fv75Z0aPHm37jzp9+nSio6N58MEH0/25paZx48Z8/PHHxMXFZWmUBqQ+bBHsG7Ka1ecOLJ9WDh8+nH79+qX4NORWFy9eTDEMc9euXSxYsIBOnTrZquk9e/Zk1KhRvPPOO/z888/JhgEahsHly5cpWrQoFStWTPUPAljmw06bNo2TJ0/aRl39/fffhIWF8cILL2T453O7vXv3Ehsbm6wXjsidKPennT8iIiLw9vZOserc999/DyRfeS8pKYmHHnqIjRs38scff9C4ceNUY+rQoQN+fn58+OGHtG7dOsW5rXkotRd1Vr179+bVV19l69atthgOHDjAihUreOmll5LtO27cOMaPH89rr72WYl7+rRo3boxhGGzbtu2OozAyatGiRdx3333JPjm8U068kx07drBv3z5Gjx6d5j7WpXutf2Mh43m2SpUq/PXXX6xatco27B6wrVJjfQOQV587sHzCe/jwYZ555pk77ieFR0HO7fbav38/Xl5elCtXDsD2Ydovv/xCx44dbftt376dAwcOZGqVpYzmh6zIaP6oUqUKhmEwe/bsZNNIb89pYMn933//PUeOHMlUfr7dokWLUozeSOu9TFpS+1lNmjSJixcvJnu+IOVz+/7776fol7Jnzx5Gjx7NK6+8QuPGjW39jrL773ZW5MRzC3n/fYEKMqm4tYFRWpYtW8Zbb71Ft27duPfee/Hx8eHIkSP8+OOPxMXF8fbbb6c4Zu7cuanO42vfvn2KddRvlV1zTevXr0/9+vWTbbMOY6tZs2ayF+ynT5+mevXqKarz48aNo1u3btx33308/PDD7Nmzh4kTJ/Lkk09SvXp1236vvvoq/fv355577uGpp57C09OTWbNmsW3bNt5//33bf+KWLVsyZMgQPvroI3bu3Ml9992Hq6srBw8eZM6cOUyYMOGO833BsvRykyZNaNmyJU899RSnTp3ik08+4b777kuRsCZOnEhERARnzpwB4H//+59t6P5zzz1n+0S0e/fuvPfee6xevZr77rsv4z/kVFiHLWaloW9Wn7vNmzczcOBAihYtStu2bVNMEWvSpIntD9BDDz2Ep6cnTZo0oUSJEuzdu5dvv/0WLy+vZE0UK1WqxPvvv8+oUaM4duwYPXr0wNfXl6NHj/Lbb7/x1FNPpXhhfbvXXnuNOXPm0Lp1a55//nmio6MZN24ctWvXTjHUffr06Rw/fpyYmBjAMtTWOnx4wIAByZYqXLZsGV5eXhlqeilipdyfev5YtWoVw4cPp3fv3oSGhhIfH8/atWuZP38+DRs2TPaJ34svvsiCBQu4//77uXz5corpPNZ9/fz8mDRpEgMGDKB+/fo8/PDDFC9enBMnTvDnn3/StGlTJk6ceMfHNXToUL777ju6dOnCSy+9hKurK59++iklS5bkxRdftO3322+/8corr9iG4d8e063PQ7NmzShatCjLly/PckHm+vXrrFy5km+++SZL57Gy5u07TVdq27YtQLIpUBnNs8OGDWPKlCncf//9PPfcc4SEhLB69WpmzZpF+/btueeee4C8+9wBLF++HMMw6N69ezo/TSlMCmpuB0vBaPr06QC2kQXW10YhISHJpqZXr1492TSZBg0a0L59e6ZNm0ZUVBT33XcfZ8+e5csvv8TT05MRI0Yku1ZGXkNnR35IT0bzx6BBgxg/fjxDhgxhx44d1KxZk+3bt/P9999Ts2ZNHnjgAdu+Xbp0wcXFheXLl2d6uW+ro0ePsm/fvmRTVTMjJCSEhx56iNq1a+Ph4cG6dev45ZdfqFu3LkOGDEm27+3P7a2jMK2so2HuvvvuZH/3c/Pvdnpy4rmFfPC+IHcXdcp7bl0e705uXx7vyJEjxptvvmnce++9RokSJQwXFxejePHiRpcuXYwVK1YkO/ZOy+MBGVo2NKektfSpdXtqS+799ttvRt26dQ13d3ejbNmyxhtvvGHEx8en2G/JkiVGy5YtjWLFihlubm5G7dq1jW+++SbVOL799lujQYMGhqenp+Hr62vUrl3beOWVV4wzZ85k6HGsXbvWaNKkieHh4WEUL17cePbZZ42oqKgU+4WEhKT5PNy+JOldd91lPPHEE+leO71lr1966SWjRo0aGXoc9rDnubP+nqf1devShRMmTDAaNWpkBAYGGi4uLkbp0qWN/v37GwcPHkw1jnnz5hnNmjUzvL29DW9vb6NatWrGs88+axw4cCBDj2PPnj3GfffdZ3h5eRlFihQx+vXrZ5w7dy7FfndaJvL2/0P33HOP0b9//wxdXwon5f6M549Dhw4ZAwcONCpWrGh4enoaHh4eRs2aNY233nrLiI6OTnZ8esu53m7lypVGhw4dDH9/f8PDw8OoVKmSMWjQIGPr1q0ZehwnT540evfubfj5+Rk+Pj5G165dU+Qqe5+H4cOHG5UrV0732ukte71w4ULDZDKlumyuvZKSkoygoCCjfv36d9wvJCQk1Zgymmf3799v9O7d2wgODjZcXV2NkJAQ46WXXjKuXbuWYt+8+Nw99NBDRrNmzTJ0fSmYCltuty5lnNrX7Uszp7YtJibGePfdd40aNWoYnp6ehr+/v9G1a1djx44dKa5lz2vozOaH9JZGtspI/jAMwzh16pTx+OOPGxUqVDDc3NyM0qVLG4MHDzYuXryYYt9u3boZbdu2Tffa6S17PXHiRMPf399ISEhI91x38uSTTxo1atQwfH19DVdXV6Ny5crGyJEjU31/k9pze7u0lr3Orb/bjnxu8/r7ApNhpLGcgEghN336dJ599llOnDiR4SZwqalRowZdu3Zl7Nix2RecpGnnzp3Ur1+f7du3Z6kPjYgUTkeOHKFatWosXrzYNuIkM4YOHcrWrVvZvHlzNkYnaTl37hwVKlTgl19+0QgZEbHb2rVradWqFfv3789S89fOnTvj4+PD7NmzszE6yaz88L5ABRmRNJjNZu666y769u3L66+/nqlzxMfH89FHH9GnT59kU7ok5zz88MOYzWb9IRSRTHvmmWc4dOhQqk1pM+rbb78lODg4xUoPkjNeffVVVqxYoQKYiGRap06dKFu2LN99912mzzF27FiaN2+eZi8WyV354X2BCjIiIiIiIiIiIrnMKf1dREREREREREQkO6kgIyIiIiIiIiKSy1SQERERERERERHJZS6OuKjZbObMmTP4+vpiMpkcEYKISK4zDIOrV69SpkwZnJwKVz1ceV9ECivlfuV+ESl8Mpr7HVKQOXPmDMHBwY64tIiIw508eZKyZcs6OoxcpbwvIoWdcr+ISOGTXu53SEHG19cXsATn5+fniBBERHJdVFQUwcHBthxYmCjvi0hhpdyfMvdPXn2YL1ccolf9IN7pXstR4YmI5JiM5n6HFGSsQxb9/Pz0wlxECp3COGxbeV9ECjvl/pu538vHFyd3L9w8ffQ3QUQKtPRyf+GayCoiIiIiInmCgeHoEEREHEoFGRERERERyTXWD4wN1WNEpJBTQUZERERERHKNCUtFRvUYESnsHNJDRiQ/SkpKIiEhwdFhSB7m6uqKs7Ozo8MQkWyk3C/pUe63n0bISF6n3C/pya7cr4KMSDoMw+DcuXNEREQ4OhTJB4oUKUKpUqUKZfNGkYJEuV/sodxvH+tPST1kJK9R7hd7ZEfuV0FGJB3WpFyiRAm8vLz0YktSZRgGMTExXLhwAYDSpUs7OCIRyQrlfskI5f7MMd2syIjkKcr9khHZmftVkBG5g6SkJFtSLlq0qKPDkTzO09MTgAsXLlCiRAkNYRfJp5T7xR7K/fZTDxnJi5T7xR7ZlfvV1FfkDqxzR728vBwcieQX1t8VzTsWyb+U+8Veyv32udlDRiUZyTuU+8Ve2ZH7VZARyQANV5SM0u+KSMGh/8+SUfpdyRyVYyQv0v9nyajs+F1RQUZERERERHKN9U2MBsiISGGngoyIiIiIiOQa9fQVEbFQQUZEMmXVqlWYTCa7lgUsX748n3/+eY7FJCIiOUu5X7KDesiI5C/K/TlHBRmRAmrQoEGYTCaefvrpFPc9++yzmEwmBg0alPuBiYhIjlHul/xAI2REspdyf/6lgoxIARYcHMwvv/zC9evXbdtiY2OZOXMm5cqVc2BkIiKSU5T7Ja+zNcJURUYk2yj3508qyIjYyTAMYuITc/0rM8N669evT3BwMPPnz7dtmz9/PuXKlaNevXq2bXFxcQwfPpwSJUrg4eFBs2bN2LJlS7JzLVq0iCpVquDp6Unr1q05duxYiuutW7eO5s2b4+npSXBwMMOHD+fatWt2xy0iktco9yv3S/bRIjaSXyj3K/fnNBdHByCS31xPSKLGm0tz/bp73+2Al5v9/2Uff/xxpkyZQr9+/QD48ccfeeyxx1i1apVtn1deeYV58+Yxbdo0QkJCGDt2LB06dODQoUMEBgZy8uRJevbsybPPPstTTz3F1q1befHFF5Nd5/Dhw3Ts2JH333+fH3/8kYsXLzJs2DCGDRvGlClTsvTYRUQcTblfuV+yn6EhMpLHKfcr9+c0jZARKeD69+/PunXrOH78OMePH2f9+vX079/fdv+1a9eYNGkS48aNo1OnTtSoUYPvvvsOT09PfvjhBwAmTZpEpUqV+OSTT6hatSr9+vVLMQ/1o48+ol+/fowYMYLQ0FCaNGnCF198wU8//URsbGxuPmQRkUJPuV/yMlsPGdVjRLKVcn/+oxEyInbydHVm77sdHHLdzChevDhdunRh6tSpGIZBly5dKFasmO3+w4cPk5CQQNOmTW3bXF1dadSoEfv27QNg37593HPPPcnO27hx42Tf79q1i927dzNjxgzbNsMwMJvNHD16lOrVq2cqfhGRvEC530K5X7LFjTlLKshIXqfcb6Hcn3NUkBGxk8lkytQQQkd6/PHHGTZsGABfffVVjlwjOjqaIUOGMHz48BT3qZGYiOR3yv2pU+6XzLi5ypIqMpK3KfenTrk/++Sv3y4RyZSOHTsSHx+PyWSiQ4fkVf5KlSrh5ubG+vXrCQkJASAhIYEtW7YwYsQIAKpXr86CBQuSHbdp06Zk39evX5+9e/dSuXLlnHsgIiKSYcr9klfZFllSPUYk2yn35y/qISNSCDg7O7Nv3z727t2Ls3PyIZDe3t4888wzvPzyyyxZsoS9e/cyePBgYmJieOKJJwB4+umnOXjwIC+//DIHDhxg5syZTJ06Ndl5Ro4cyYYNGxg2bBg7d+7k4MGD/PHHH7YKvYiI5C7lfsmrTDfGyKgeI5L9lPvzFxVkRAoJPz8//Pz8Ur3v448/plevXgwYMID69etz6NAhli5dSkBAAGAZejhv3jx+//136tSpwzfffMOHH36Y7Bx33XUXq1evJiwsjObNm1OvXj3efPNNypQpk+OPTUREUqfcL3mRRsiI5Czl/vzDZGRmkfMsioqKwt/fn8jIyDR/UUTygtjYWI4ePUqFChXw8PBwdDiSD9zpd6Yw577C/Ngl/1HuF3sp96curcf+y+YTvDr/X9pVL8H3j97twAhFblLuF3tlR+7XCBkREREREck1GiEjImKhgoyIiIiIiOQa9ZAREbFQQUZERERERHKPbYSMSjIiUripICMiIiIiIrnmRj1GI2REpNBTQUZERERERHKN6UYTGQ2QEZHCTgUZERERERHJNRohIyJioYKMiIiIiIjkGpN6yIiIACrIiIiIiIhILrIWZERECjsVZEREREREJNfYlr3WABkRKeRUkBGRHBUTE0OvXr3w8/PDZDIRERHhsFhWrVrl8BhERAo65X1Jj0bIiBQ8yv2Zo4KMSAFkMpnu+PX222/nWizTpk1j7dq1bNiwgbNnz+Lv758r123VqhUjRoxItq1Jkya5GoOISG5R3lfez48MtfUVyRLl/vyf+10cHYCIZL+zZ8/abv/666+8+eabHDhwwLbNx8fHdtswDJKSknBxyZl0cPjwYapXr06tWrVy5Pz2cHNzo1SpUo4OQ0Qk2ynvp055P2/TlCWRrFHuT11+yv0aISNiL8OA+Gu5/2XHq5ZSpUrZvvz9/TGZTLbv9+/fj6+vL4sXL6ZBgwa4u7uzbt06Bg0aRI8ePZKdZ8SIEbRq1cr2vdls5qOPPqJChQp4enpSp04d5s6dm2YcrVq14pNPPmHNmjWYTCbbuUwmE7///nuyfYsUKcLUqVMBOHbsGCaTifnz59O6dWu8vLyoU6cOGzduTHbM+vXradWqFV5eXgQEBNChQweuXLnCoEGDWL16NRMmTLB9QnDs2LFUhy/OmzePmjVr4u7uTvny5fnkk0+SXaN8+fJ8+OGHPP744/j6+lKuXDm+/fbbDD0PIlKA5PHcr7yvvJ+fmEzqISP5hHK/cn8O0wgZEXslxMCHZXL/uq+dATfvbDvdq6++yvjx46lYsSIBAQEZOuajjz7i559/5ptvviE0NJQ1a9bQv39/ihcvTsuWLVPsP3/+fF599VX27NnD/PnzcXNzsyvG119/nfHjxxMaGsrrr79O3759OXToEC4uLuzcuZO2bdvy+OOPM2HCBFxcXFi5ciVJSUlMmDCBsLAwatWqxbvvvgtA8eLFOXbsWLLzb9u2jT59+vD222/z0EMPsWHDBoYOHUrRokUZNGiQbb9PPvmE9957j9dee425c+fyzDPP0LJlS6pWrWrX4xGRfKwA5H7lfeX9vMLaQkZTliTPU+5X7s/h3K+CjEgh9e6779K+ffsM7x8XF8eHH37I8uXLady4MQAVK1Zk3bp1TJ48OdXkHBgYiJeXV6aHDb700kt06dIFgHfeeYeaNWty6NAhqlWrxtixY2nYsCFff/21bf+aNWvabru5ueHl5XXH63766ae0bduW0aNHA1ClShX27t3LuHHjkiXnzp07M3ToUABGjhzJZ599xsqVK/XCXETyFeV95f28wtrUt6CPkLl4NY51hy5Subgvtcvm/V4WUjAp9+ft3K+CjIi9XL0sVWtHXDcbNWzY0K79Dx06RExMTIqEHh8fT7169bIzNJu77rrLdrt06dIAXLhwgWrVqrFz504efPDBLJ1/3759dO/ePdm2pk2b8vnnn5OUlISzs3OKOKxDQS9cuJCla4tIPlMAcr/yvvJ+XmFb9trBceQEwzD4edNxft95hu0nrmAY4OPuwvpX2+Dv6ero8MReyv02yv05QwUZEXuZTNk6dchRvL2TPwYnJyeM2z6qSkhIsN2Ojo4G4M8//yQoKCjZfu7u7nZd22Qy3fFaVq6uN1+4WOebm81mADw9Pe26ZlbcGoc1FmscIlJIFIDcr7yfccr7Oct0c85SgTN760lG//Gf7XsPVyei4xL5ZfMJhrSs5MDIJFOU+5Ptp9yf/dTUV0QAy3zLWzu1A+zcudN2u0aNGri7u3PixAkqV66c7Cs4ODhL1zp48CAxMTF2neOuu+7i77//TvN+Nzc3kpKS7niO6tWrs379+mTb1q9fT5UqVWyVchGRgkp530J5P/cV5B4yc7aeAqBvo3JsGtWWd7tbVpyZuuEYCUkq6onjKfdb5JXcr4KMiADQpk0btm7dyk8//cTBgwd566232LNnj+1+X19fXnrpJV544QWmTZvG4cOH2b59O19++SXTpk2z+1oTJ05kx44dbN26laeffjpFRTo9o0aNYsuWLQwdOpTdu3ezf/9+Jk2axKVLlwBLp/R//vmHY8eOcenSpVSr2y+++CJ///037733HmFhYUybNo2JEyfy0ksv2RWLiEh+pLyvvO8oBbWHzPHwa2w9fgUnE4xoF0opfw+61y1DMR93zkbGsujfs+mfRCSHKffnrdyvgoyIANChQwdGjx7NK6+8wt13383Vq1cZOHBgsn3ee+89Ro8ezUcffUT16tXp2LEjf/75JxUqVLDrWp988gnBwcE0b96cRx55hJdeegkvL/vmylapUoW//vqLXbt20ahRIxo3bswff/yBi4tlJuZLL72Es7MzNWrUoHjx4pw4cSLFOerXr8/s2bP55ZdfqFWrFm+++SbvvvtusuZeIiIFlfK+8r7jFMweMr/tOA1A08rFKOnnAYC7izOPNg4B4Lu1R1JM3xDJbcr9eSv3mwwHZIWoqCj8/f2JjIzEz88vty8vkmGxsbEcPXqUChUq4OHh4ehwJB+40+9MYc59hfmxS/6j3C/2Uu5PXVqPfel/5xgyfRv1yxVh/tCmDoww+xiGQavxqzgeHsOnferQs35Z232Xr8XT5OO/iU0w88tT93JvxaIOjFTSotwv9sqO3K8RMiIiIiIikmsKYk/f7SciOB4eg6erMx1qJl9+N9DbjV43CjTfrz3qiPBEJI9SQUZERERERHKNdRWVgjR757cdlma+nWqVwts95UK2jzezTPX4e/95Tkdcz9XYRCTvUkFGRERERERyTUEbIROfaGbhbkvD3gfqB6W6T6XiPtQp649hwNZjl3MzPBHJw1SQERERERGRXGOyVWQKRklm5YELRMQkUNLPnSaViqW5X71yAQDsOBGRS5GJSF6ngoyIiIiIiOQa27LXjg0j2yzbex6A++8qg7OTKc396pUrAsCOkxG5EJWI5AcqyIiIiIiISK4xkXbRIj/aeaPA0rjSnVdPqn9jhMzeM5HEJiTldFgikg+oICMiIiIiIrmuIMxYiopN4PDFaADqBBe5475lAzwp6u1GQpLBf2eiciE6EcnrVJAREREREZHcY5uylP8rMntORWIYlmJLMR/3O+5rMpluTls6cSUXohORvE4FGRERERERyTUFqaevtR9MeqNjrGyNfdVHRkRQQUZEHMBkMvH77787OgwREclFyv1iZbrR1bcgFGR23Sis1C1bJEP717tRuNmplZakkFDuvzMVZEQKqIsXL/LMM89Qrlw53N3dKVWqFB06dGD9+vWODk1ERHKIcr/kB7YRMg6NInvsOhUBQN0bU5HSc1dwEUwmOB1xnQtRsTkXmBQqyv35l4ujAxApTMLC4PBhqFwZQkNz9lq9evUiPj6eadOmUbFiRc6fP8/ff/9NeHh4zl5YRERscjPvg3K/5A+2Za/z+RCZs5HXOR8Vh7OTiZpl/DJ0jI+7C1VL+rL/3FV2nIygQ81SORylOIJyv2SURsiI5ILLl6FjJ4OqVaFzZ6hSxfL9lRzq5xYREcHatWsZM2YMrVu3JiQkhEaNGjFq1Ci6desGwKeffkrt2rXx9vYmODiYoUOHEh0dbTvH1KlTKVKkCAsXLqRq1ap4eXnRu3dvYmJimDZtGuXLlycgIIDhw4eTlHRz6cby5cvz3nvv0bdvX7y9vQkKCuKrr766Y7wnT56kT58+FClShMDAQLp3786xY8ds969atYpGjRrh7e1NkSJFaNq0KcePH8/eH5qISDbK7bwPyv2SfxSUZa+t05WqlPTFyy3jn3PfbOwbkf1BiUMp9yv320sFGZFc8Eg/gxVrEinadQdBz/xN0a47WLEmkb6P5MwnQz4+Pvj4+PD7778TFxeX6j5OTk588cUX/Pfff0ybNo0VK1bwyiuvJNsnJiaGL774gl9++YUlS5awatUqHnjgARYtWsSiRYuYPn06kydPZu7cucmOGzduHHXq1GHHjh28+uqrPP/88yxbtizVOBISEujQoQO+vr6sXbuW9evX4+PjQ8eOHYmPjycxMZEePXrQsmVLdu/ezcaNG3nqqads889FRPKi3M77oNwv+cfNETKOjSOrdp6MBKBuBhv6WtULvtHYVystFTjK/cr9djMcIDIy0gCMyMhIR1xeJMOuX79u7N2717h+/Xqmz3HggGGAYRTtut0IGbnQ9lW06w4DDCMsLBsDvsXcuXONgIAAw8PDw2jSpIkxatQoY9euXWnuP2fOHKNo0aK276dMmWIAxqFDh2zbhgwZYnh5eRlXr161bevQoYMxZMgQ2/chISFGx44dk537oYceMjp16mT7HjB+++03wzAMY/r06UbVqlUNs9lsuz8uLs7w9PQ0li5daoSHhxuAsWrVKvt/CA5wp9+Zwpz7CvNjl/wnq7nfUXnfMJT7HUW5P3VpPfb1By8aISMXGu0/zR/Pb1oemrzBCBm50Phl83G7jgs7F2WEjFxoVHtjsZGQmJRD0Ym9lPuV++2VHblfI2REctjhw5Z/PYIvJ9vuEWyZ03noUM5ct1evXpw5c4YFCxbQsWNHVq1aRf369Zk6dSoAy5cvp23btgQFBeHr68uAAQMIDw8nJibGdg4vLy8qVapk+75kyZKUL18eHx+fZNsuXLiQ7NqNGzdO8f2+fftSjXPXrl0cOnQIX19fW4U/MDCQ2NhYDh8+TGBgIIMGDaJDhw7cf//9TJgwgbNnz2b1xyMikmMclfdBuV/yiQIwQibJbPDvKcsImYwueW1VqbgPvu4uXE9I4sD5qzkQnTiCcv/N75X7M04FGZEcZs1rsScDk22PPVkUsDT7yikeHh60b9+e0aNHs2HDBgYNGsRbb73FsWPH6Nq1K3fddRfz5s1j27Zttvme8fHxtuNdXV2Tnc9kMqW6zWw2ZzrG6OhoGjRowM6dO5N9hYWF8cgjjwAwZcoUNm7cSJMmTfj111+pUqUKmzZtyvQ1RURykiPzPij3S95n7SGTj+sxHL4YzbX4JLzcnAkt4WvXsU5OJlsRZ/eNoo7kf8r96VPuT0kFGZEcVqUKdOhoELWiFtH/BZEY5UH0f0FErahJh45GrnRet6pRowbXrl1j27ZtmM1mPvnkE+69916qVKnCmTNnsu06tyfNTZs2Ub169VT3rV+/PgcPHqREiRJUrlw52Ze/v79tv3r16jFq1Cg2bNhArVq1mDlzZrbFKyKSnfJS3gflfsl7CsIqSztvNOStHeSPs5P9/S2qlLQUcQ5fiE5nT8kvlPtvfq/cn3EqyIjkglkzTbRp4UL4wrqcntSW8IV1adPChVkzc6ZBVXh4OG3atOHnn39m9+7dHD16lDlz5jB27Fi6d+9O5cqVSUhI4Msvv+TIkSNMnz6db775Jtuuv379esaOHUtYWBhfffUVc+bM4fnnn0913379+lGsWDG6d+/O2rVrOXr0KKtWrWL48OGcOnWKo0ePMmrUKDZu3Mjx48f566+/OHjwYJqJXkQkL8jtvA/K/ZJ/WP8X5N9yDOw8FQHY39DXqmJxb8Ay0kYKDuV+5X57ZXx9NhHJtIAAWLLYxMGDlvmjlStDaGjOJWYfHx/uuecePvvsMw4fPkxCQgLBwcEMHjyY1157DU9PTz799FPGjBnDqFGjaNGiBR999BEDBw7Mluu/+OKLbN26lXfeeQc/Pz8+/fRTOnTokOq+Xl5erFmzhpEjR9KzZ0+uXr1KUFAQbdu2xc/Pj+vXr7N//36mTZtGeHg4pUuX5tlnn2XIkCHZEquISE7I7bwPyv2Sf9hWTMnHFZndNwoy9vaPsapU3NKX48ila9kUkeQFyv3K/fYyGQ4YKxgVFYW/vz+RkZH4+fnl9uVFMiw2NpajR49SoUIFPDw8HB1OvlC+fHlGjBjBiBEjHB2KQ9zpd6Yw577C/Ngl/1Hut59yv3J/atJ67FuOXebBbzZSoZg3K19q5bgAMynJbFDjzSXEJZpZ9VIryhfztvscF6JiafTh3ziZYO+7HfFwdc6BSMUeyv32U+7Peu7XlCUREREREck1tilL+bSHzInLMcQlmnF3cSI40CtT5yju646vuwtmA46Hx6R/gIgUSCrIiIiIiIhIrsnvM5bCbixVHVrSJ1MNfcEybcvaR+aI+siIFFrqISMi2erYsWOODkFERHKZcr/YJ2d7auS0sHOWgox1paTMqlTch12nItXYV/It5f6s0wgZERERERHJdfl0xhIHzmdPQebmCBk19hUprFSQEckAs9ns6BAkn9DvikjBof/PklH6XbHPzSlL+bMic/C8ZURL1WwYIQNa+jqv0f9nyajs+F3RlCWRO3Bzc8PJyYkzZ85QvHhx3Nzcbi7VKHILwzCIj4/n4sWLODk54ebm5uiQRCSTlPslo5T7M+dmU1+HhpEpCUlmjlyyFFBCS/pk6VyVStxY+vriNQzDUJ5xMOV+yajszP0qyIjcgZOTExUqVODs2bOcOXPG0eFIPuDl5UW5cuVwctIARJH8Srlf7KXcbx/rm9z8WJA5dukaCUkG3m7OBBXxzNK5Qop64WSCq3GJXLwaRwk/LbXsSMr9Yq/syP0qyIikw83NjXLlypGYmEhSUpKjw5E8zNnZGRcXF32aIlIAKPdLRin32y8//6Rs/WNK+Wb5OXd3cSY40Ivj4TEcvnhNBZk8QLlfMiq7cr8KMiIZYDKZcHV1xdXV1dGhiIhILlHuF8kZth4y+XCIjG2FpRJZ6x9jVbGY942CTDSNKxXNlnNK1ij3S27SuEoREREREck1phtjZPJfOQbCbjT0rVIqewoy1sa+WmlJpHBSQUZERERERHLNzREyjo0jM8JsS15nraGvVUWttCRSqBX4KUthYXD4MFSuDKGhjo5GRERyg3K/iEjel93LXud07o9NSOJYuGUkS1aXvLaqVNwbUEFGpLAqsCNkLl+Gjp0MqlaFzp2hShXL91euODoyERHJKcr9IiJ5X3aPkMmt3H/4YjRmA4p4uVLc1z1bzmkdIXM64jqxCWoiK1LYFNgRMo/0M1ixJpGiXffgEXyZ2JOBrFhRi76PuLBkcX7u7S4iImlR7hcRyfuyu4dMbuV+23SlEllfYcmqmI8bfh4uRMUmcvTSNaqX9suW84pI/lAgR8iEhcHSJSb82uzBp+YZXPxi8al5Br82/7F0iYmDBx0doYiIZDflfhGR/CE7R8jkZu6/2dA3e/rHgGVFn4pq7CtSaBXIgszhw5Z/PYIvJ9vuERwOwKFDuR2RiIjkNOV+EZH84ebgkqxXZG7m/vBk23Mi99uWvM6m/jFWldTYV6TQKpAFmUqVLP/GngxMtj32ZFHA0uhLREQKFuV+EZH8wTZlKRtGyFSqBAHt9uDsE5dse07k/gPnc6YgU/FGY9+jlzRCRqSwyVMFmbAwWLyYLA8trFIFOnQ0iFpRi+j/gkiM8iD6vyCiVtSkQ0dDK26IiOQhyv0iIoWLdYRMXHz25P7Au85huu1dTcLpgGzN/dfiEjl15brlmtlckAkO9ALg5OWYbD2viOR9eaIgkxOd0WfNNNGmhQvhC+tyelJbwhfWpU0LF2bNVFNHEZG8QLlfRKTwuXwZhgyxDI2JjDSynPtjE5JIdLWMjrmyshpxZ4oAUO7u8GzN/YcuWKYTFfNxJ9DbLdvOCxAc4AnAySsqyIgUNnlilaWc6IweEABLFlsaeR06ZBmuGBqqF+QiInmFcr+ISOHzSD+Df/5NokQ1cPJIoGjXHVnK/WciLKNWvNyc+Wt6RRZt9efz3f/gW/4KAQHZF/fN6UrZ19DXyjpC5nxUHLEJSXi4Omf7NUQkb3J4QcbaGb1oV0tndODGvyaWLqzLwYNkaahhaGjWjhcRkeyn3C8iUvhYc3+xnpZOuyanrOf+kzemEQUHeFGliomgkCJ8ucfEmchYzkRcp0wRz2yJ/WAO9Y8BKOrthqerM9cTkjgdcd3W5FdECj6HT1nSqhgiIoWPcr+ISOFjzf3upSKSbc9K7j91Y5pP2RvTfrzdXahe2lI02X4iC3Ngb2Nd8jo0B0bImEwmggNvTFtSHxmRQsXhBRmtiiEiUvgo94uIFD7W3B93tkiy7VnJ/Scv3xghc2PaD0CDcpa5StuOZ19BJidHyIBlhA/cHPEjIoWDwwsyWhVDRKTwUe4XESl8rLk/en1VwLLsdVZz/+0jZADqh1gKMttPRGQ5ZoCrsQmciYwFoEqJHCrI3CgondIIGZFCxeE9ZMCyKkbfR1xYurCubVuHjoZWxRARKWCmbzxGDG5cvhZPtQFwLghOHHchek9ZkqI8adTlCmM+9sYwvDCZ9DdARKSgmTXTRO+BrhwGMJsIX1g3S6/7rSNKygbcHCFT/8YImf9OR2ZLk9yDN1ZYKuHrjr+Xa5bOlRbb0tdaaUmkUMkTBRmtiiEiUjiMWXIAJ/ebL5opBn7Fbn57Cuj+Lfh7unJXWX/qlQugZZXi1A0ugrOT/i6IiOR3AQGWokyjD8DJ2SAsLGuv+0/fKGBYe7CAZbRMCV93LlyNY/epSBpVCEzr8AzJ6elKcMvS15c1ZUmkMMkTBRkrrYohIlKwdahZkjLFAwn0dsfF2URikkGi2cyVmHjORFhWxDhy6RqR1xNYe/ASaw9e4ou/D1LMx43WVUvQvW4QTSoVxUnFGRGRfMv5xghIA6hc2QAyl9Nj4hO5FB0PJB8hYzKZaBASwOI959h2/EqWCzLWhr45WpDRCBmRQsmxBZnDK6BIIHgVBd/S4BkAGqIuIlJgfVLnLH5F4sDFA7yLgW8p8CiSLPcnJJk5cO4qO09GsOlIOKsPXORSdDxztp1izrZTlA3w5KGGwTx0dzAl/Dwc92BERCRjDiyGIkXB1QO8i+PsUhRLOcZEktnAxTlzr/9P35iu5Ofhgr9n8qlEtxZksirMNkIm55ajthZkImISuBqbgK9HzkyNEpG8xbEFmdkDwf2WBOzsDkXKQYlqULw6lKwJwfeAX2nHxSgiItln/uDkeR8sxZkiIbbc71qqFrWC76FWUAj97w0hPtHMlmOXWfTvWRbsOsOpK9f5ZFkYX644RK8GZXm6ZUVCino75vGIiEj6bsv9RYC97u6cMEpgmjcHStaAkrUsr/u9i2b4tCdtDX29UtxX70YfmR0nrmAYRpb6kh20LXmdcyNkfNxdCPBy5UpMAicvX6dGGRVkRAoDxxZkStYClwS4dgmuX4akOAg/aPna97+b+wWUh3JNILQdVG4HHv4OC1lERLIgqKEl7ydch2sXITYCEmPh0gHLF3/c3DewEoQ0wS20PU0rtaFp5dq80aUGi/ecZcY/J9h2/AqzNp/g1y0n6FanDC/eVzXZsqciIpJHlGkAromQEHMj90fiZYqjmukk7D0Je3+7uW+xqhDSGEI7QMVW4JZ2Xj91xbrktWeK+2oF+eHm7ET4tXiOh8dQvljmCveR1xM4F2VZYSk0B0fIgGWUzJWYSE5eiaFGGb8cvZaI5A2OLcg8vgT8biSbhFiIPgeXj8CF/XBhL5zdCef2wJVjlq9dM8HJBUKaQM0HLF+eAQ58ACIiYpeBv9/M+2ApzFw9C+FH4OI+S/4/s8PyN+DyYcvXjung7Ablm+NZqyc9a3SjZ/0mbD56ma9XHWLVgYv8vvMMi/49x6NNQhjWOjTHVsEQEZFMePSPZLk/NuYqHd6bTQXTWSZ38ML9chic3n6zOH/pAGybahlBWaEl1OoF1buCW/KiysnLaY+QcXdxpnZZf7Ydv8K241cyXZCxNvQt7e+BXw5PIwoO8GL3qUjb4xKRgi/vNPV19bCMhAkoD5Xa3NweGwknt8DR1RC2BC6FwdE1lq/Fr0LVTlBvgOUYJydHRS8iIpnh6gmBFS1foe1ubr9+BU5uhiOr4cAiuHIUDv9t+frzJajelUb1B9JoUHP2nIni48X7WXfoEt+tPcqcbacY1akafRoGa+lsEZE8yMnNm+NGKY4bpYhtdB/u1v4v18Lh5CY4sgoOLIHIE3BwqeXrTx+o0R3qD7RMbTKZbCsSWVcoul2DkAC2Hb/C1uNX6NWgbKZiDcuF6UpWZW+M9LGO/BGRgi/vFGTS4uFveZEe2g7uew/CD8P+hbDrF8snqHt/t3wVDYV7hkCdvuCes8MJRUQkh3kGQJUOlq8OH1iK8fv+Z8n94Qfh3zmWrxI1qXXPEKYPfJDVR6P5cNE+ws5HM3Lev8zbfpoPH6hN5RL6myAikpc437JSntls3LzDuyhU62L56jT2xmv9BbD7F8to+Z0zLF+l68I9T3PuSkkg9REyAPWCiwCw+1REpmO1NfTNhb8lwTcexymttCRSaOS/ISVFK0HT5+GZDTBkDTQaAu5+lhfoi16Cz2rAqjGWkTUiIpL/mUxQvCq0eAmGbYEnV0DDx8HVCy78B/8bjunzWrS6OJNFT9fjjS7V8XR1ZvPRy3SesJavVh4i6dYX/CIi4lC31GNIMtLIzyaTZYGP1qNg+E54bAnU7W+ZxnR2J/z+NN9efpzHnBdTzi/10ZC1gix9J8POXyUuMSlTsR68cKMgUyrnR8jYlr6+rBEyIoVF/ivIWJlMULoOdB4L/7cXOo2zNICMjYRVH8JntWHVxxB31dGRiohIdjGZoGwD6PoZ/N8+uO99y+p8MeGw/C1cvqzLk6Y/WP5cQ9pUK0F8kplxSw/w8LcbNSdfRCSPMJlMtqKMOSMFc5PJ0ui3x1fwwl5o+yZm39KU4ApvuU6n8qxmsPFrSIxLdljZAE+KeLmSkGQQdi46U7FapyxVyYUpS9apVyevxGCkVagSkQIl/xZkbuXuC/c8ZfnktPePULwaxEXCqo/gi/qwdQokJTo6ShERyU6eRaDJc/DcDugxydKHJiYclr9N0M8t+KHuQcb3ro2Puwtbjl2h04S1/LbjlKOjFhERbk5bSnOETFq8i0LzF9nfZx2jEp7gLMVwunYelo6CiXfDf7/BjXOaTCZqlbGMkvn3tP2j5yNi4rl41VLkCc2FKUtBAZ6YTBATn8Tla/E5fj0RcbyCUZCxcnK2dGF/ZiP0nmIZMXPtAiwcAd80szSHFBGRgsXZBeo+As9ugR7fgH85iDqN6fdn6L2tP3/38eDu8gFExyXywq+7GDX/X2ITMjd0XUREsofTjabrmZ1SeioqkVlJbXm26PfQ9XPwKQURx2HOIPixA5zZCdyctrTnjP0FmQPnLCPtg4p44u2e86033V2cKenrAcBJNfYVKRQKVEEmLAwWL4aDh52gVk8Yugk6fmxpDnlxH/zUDeY/BdEXHR2qiIhkE1vuP+ICdftaRku2e9vSX+zsLkrO6cavZX5lZMsSmEwwa/MJen+zQVOYREQcyDZCJpMFme1hloKFj5s/NHwMhm+HVqMs/cVO/gPftYYlo6hbwhmAPZkYIbP7lOWYWkF+6eyZfYJvrLSkv1EihUOBKMhcvgwdOxlUrQqdO0OVKpbvr1x1g3ufgeE74O7BgAl2/woTG8L26bbhjCIikv+kmfujPaDZC5bcX68/AE7bp/LMvw/zZ+sLBHi6sOd0FF2/XMeGQ5cc/ChERAqnzBZkrLl/7FeWgsX/fvG05P5r3tDqVXhuu2XEvGGGTV/TbsX9tHPaxv6zV4lPNNt1rV03Vme6q2wRu47LCutKSye10pJIoVAgCjKP9DNYsSaRol13EPTM3xTtuoMVaxLp+8iNBO8ZAF3Gw5N/Q6naEBsBC4bBzIfg6jmHxi4iIpmTbu73Lgbdv4JBi6BYVYi5RI0NI9hQeTrNgkxEXk9g4I+b+XnTccc+EBGRQshakDHb+QGpNfd7VbG8hncPDk+e+/1KW3pK9p8PARVwuXaW790+4QPT1xw+ddqua1kLMnVysSBTVistiRQq+b4gExYGS5eY8GuzB5+aZ3Dxi8Wn5hn82vzH0iUmDh68ZeeyDWDwKmj/Lji7wcGl8NU9sGeeo8IXEZFMsCv3l28KT6+zDGV3csHz4P+YHjuc1ysdI9Fs8Mbve3jrjz0kJtn3yamIiGSes62HTMaPuTX3u/jFAuBRJjL13F+5LQzdCE2fx4yJB13WEPJLWzi8MkPXunwt3lYUqV3WP+NBZpF1paVTGiEjUijk+4LM4cOWfz2CLyfb7hEcDsChQ7cd4OwCTZ+HIWssy2bHRsDcx+GPYRCvxCcikh/Ynftd3CxD2Z9cDsWrYbp2kcGnX+OPSgtwI4FpG4/z9M/buR6vZr8iIrnBKRNTlm7m/vBk29PM/a6e0P5dfq7+DcfMJfGKPQ/TH4Dl76S7Aqt1dEzFYt74e7pmOMasCraNkNH7EpHCIN8XZCpVsvwbezIw2fbYk0UBqFw5jQNLVLdMYWrxMmCCHdMtzb8u7Mu5YEVEJFtkOveXqQdPrYbGwwCoc/oXtpQaS6jLBZbvO88j32/SUqMiIrnAOkLGnilLttx/OiDZ9vRyf5FqLegU/xFLPDoBBqz7FKZ2gchTaV5r90lLQ986wUUyHF92CCpiGSFzJjIWcyYbHotI/pHvCzJVqkCHjgZRK2oR/V8QiVEeRP8XRNSKmnToaBAaeoeDnV2hzRsw8A/wKQkX98O3rWH3nFyLX0RE7Jel3O/qAR0+gEdmg2cg/hH/scTzDXp47GDHiQh6T9IKTCIiOS0zTX2tuT96YxXAsj5H9H9l0s39tYP8uY4Hz0c/SlKvKZZV+E5ugm+aweEVqR6z29bQN/emKwGU8vfAyQTxiWYuXYvL1WuLSO7L9wUZgFkzTbRp4UL4wrqcntSW8IV1adPChVkzTRk7QcWW8PR6qNQGEq/D/CdhyWvpDmUUERHHyXLur9LB0lumXBOcE6L5nHG85f0bRy9dpc/kjRy+GJ2zD0BEpBBzuvEuJMnOpr6zZppo3MRy2xzrSvjCeunm/pBAL3zdXYhLNBNWrJ2ldUGZenD9CvzcC9Z9nmz1VcMwHLLCEoCrsxMl/TwAOBMRm6vXFpHcVyAKMgEBsGSxibAwWLTI0vBryWITAQHpH2vjUxz6zYXmL1m+3/QVTO8B1yxzUsPCYPFikjcLExERh8mW3O8fBI8ugHueAeCxpDnM8vmc6MjL9PlmI4s3Rin3i4jkANuUJTun5QQEwGdfWvp9FS/ikqHc7+RkomaQHwB7TkdCYAV4bAnU629ZHnv5WzD3MYi/BsD6HbFcio7H2WSiZhm/TDy6rClzY9rS6StaaUmkoCsQBRmr0FDo1Ik7D1W/EydnaDsa+kwHNx84tpakyW148oEDVK0KnTtbhkp27GRw5Uq2hi4iIpmU5dzv7AqdPoYHvgUXD+5N3MpCr3fxjDnFU79upMeTV5T7RUSyWWaa+lpdi7OMYi9exCXDub9WGcvUoz2nLb1hcPWAbhOhy6fg5Ar//Ubid514pNsZOjwSAUDMWV96dHPK9dxv7SNzOkLTZ0UKugJVkMk2NbpZGv4GlMc56hjjqranR9/vCXrmb4p23cGKNYn0fURNtkRECpQ6D8HjS8G3DCHmE/zu8hZ3e+6lVP8NFH/wH+V+EZFsZFv22s4pSwBXYy0FGR8PlwwfY126+l9rQQbAZIK7n4BBC8GrGC4XdzE2tA1NWi8BwMkt0SG5P+jG0teasiRS8Kkgk5YS1Tjc+m/Wn7iHAI9IZoe+Qt+AJfjUPINfm/9YusSkIewiIgVNmbocafs328/eRTHnSGa5fUBX5014VbxEkS47lPtFRLKJtamv2Wz/sdYRMt7udhRkgm6MkDkTRUz8bX0iy93L0XbL2XuxKmV9z/J7iZG0dtqBa2CMQ173W6csndKUJZECTwWZOwg7XYy2Py3g99jmuJqSGOf6LUOdf8cj+BIAhw45OEAREcl2B86WocWUxSyNuxt3UwJfun7Jo85L8axwEbcyV5T7RUSygVMWRshE3yjI+NpRkKlQzJvgQE/iE82sO3gpxf37z1egyQ9/sTa+Nt6mOL5z/YTezqvxCLb0k8zN3F/WNmVJBRmRgk4FmTuoVAnikjx48r93+SqxGwCvuM7mTWZgwkzlyg4OUEREsl2lSnAtwYcBez5mWmJ7nEwG77hO42XXXynZ5x+MIpHpn0RERO7o5giZzBdkvN2dM3yMyWSibbWSACzfdz7F/ZUqQWRcEfqEjWVeUnNcTGbGu05mcPxSwMjV1/03pyypICNS0KkgcwdVqkCHjgZRK2rz1q4Xeevq4wA8VWI+K4Y9QWjFBAdHKCIi2c2a+yNW1OHFXa8zNrovAMNc/mCM9zeM/msDYeevOjhKEZH8LStNfa0FGR93V7uOa1/DUpBZsf9CikKQNffHHC3DiwlPMyn+fgDeKjuZeU+9Rmjl3OsjY52yFHk9wfZYRaRgUkEmHbNmmmjTwoXwhXV599PPeHjuDySYXWlVdD78OgAS1GxLRKSguZn76zHyk294csEXJBlO9HVZyZuJX/Dod+s5dumao8MUEcm3nC31mMxNWbI29bVjhAxAowqB+Hq4cCk6np2nIlLcP2umibL3XABMvLb+DV5Y+iEAPUt/Df97HsxJdseaGT7uLvh7WopNWvpapGBTQeaGsDBYvJgUDbsCAmDJYhNhYbBoEbz3W29cB8wCFw8IWwyzHoJ4vSgXEcmPMpr7R/76KM59pmA4udDdeQPvxI1l0HfrOBeporyISGZkZcqStamvPassAbg6O9GqagkAJv/vfIrcH+t0nev+FwH4bHhZhv70LHT/GkxOsH0a/PY0JOXOiBXrKBlNWxIp2Ap9QebyZejYyaBqVejc2TJcsWMngytXku8XGgqdOln+JbQ99JsLrt5wZBX83AviNHxdRCS/yFTur9kD08MzMZzduc95G+/EvM+TP6whIibeIY9BRCQ/szb1TcxEQeZqJlZZAkvu37bAUpD53/bzKXL/7C2nMBtwT4VABvXyseT+ev2g1/fg5AL/zoa5gyAp59sWBFlXWlJBRqRAK/QFmUf6GaxYk0jRrjsIeuZvinbdwYo1ifR9JJ0/DhWaw8A/wN0fTmyEn3urKCMikk9kOvdX6YCp3xzMrl60dN7NK1fe5ekp67genzvD2EVECgrbCJlMTFmyjZCxsyDzSD+DbUsDMAxwKx5NsQe22HJ/ktlg9taTADzcKDj5gbV6wUM/g7Mb7PsfzBmU40WZsjca+2rKkkjBVqgLMmFhsHSJCb82e/CpeQYXv1h8ap7Br81/LF1iSjGMMYXgu+HRP8DDH05ughkPqigjIpLHZTn3V2yJU/95mF28aOH8L8+ce4vhP28kIcmcK/GLiBQEztnS1DfjBRlr7vdteoAbg3PwrnLBlvt/XX2J0xHX8fNwoVOt0ilPULUT9J0Fzu6wfyHMfSxHizJlingAmrIkUtAV6oLM4cOWfz2CLyfb7hEcDsChQxk4SZl6MOD3myNlZjwIcdHZG6iIiGSbbMn9IU1w6j+XJBdPWjrvpv/RUbw5dytGJj7pFREpjHK7IJNe7p+77QQAPeuXxcM1jWbBldvBwzNujpSZ+3iOFWWCingBcFoFGZECrVAXZCpVsvwbezIw2fbYk0UBqFw5gycKqg8Df7tZlPmlr1ZfEhHJo7It95dvinP/uSQ5W4oybfaM5Mtl+7IxUhGRgsvZlPkpS9ZVluzpIZNW7jfHu+AedJndl88D8NDdwbcfmlxoe3jIWpRZAL8/kyOrL2mEjEjhUKgLMlWqQIeOBlErahH9XxCJUR5E/xdE1IqadOhoWBp5ZVRQAxgwH9x84OgamD0QEtXoUUQkr8nW3F++Gc79Z5Po5E575+2UX/t/zNlyLKdCFxEpMJxsI2TsP9baQ8bXjlWWbs/95gTL2yC3YtGU6r+RRLNBneAiVC/tl4GT3Qd9frrR6HcOLHwBsnmEZNCNHjLno2I1JVakACvUBRmAWTNNtGnhQvjCupye1JbwhXVp08KFWTNN9p+sbEN45FfLktgHl8JvT+VIxVxERLImW3N/hRa4PPwzSSYXujlvxFgwgjUHzmd/0CIiBYh1hEySnYUMs9ng2o1G6vY29b0195/8rAMX5jXEO6o41sw/8N6QjJ+saifo+e3NJbGXvp6tRZli3u64uThhNuBcpEbeixRU9mWxAiggAJYstjRxPHTIMlQ9NDQTL8ityjezDGOc9TD895tlxEy3L7F1DxMREYfL9txf5T6cev+Aec5j9HFeyU8zX6DUM99QpVQGPmkVESmEbKss2dlD5lp8ou22vcteJ8/9TlSuXJLQ0JKcuhLDycvXubdiYPonuVWtXhAfAwuGwaavwMMPWr1q3znS4ORkooy/B8fCYzgdcZ3gQK9sOa+I5C2FfoSMVWgodOqEfUPV0zxZO+j9o6VivmM6/P1uNpxURESyW3bmflPNHiTd/yUAA01/8vf3r3EpOi7rJxYRKYCcMtnU19rQ19XZhLtL5t7K3J77ywZ40bhSUUyZ+QC1/gDoOMZye9VHsOWHTMWUmiAtfS1S4Kkgk1NqdIOun1tur/sUNn7t0HBERCTnuTboT0wrSxH+mcTpzJr8IbEJmroqInI75xu1D3ub+lr7x3i7u2SugJIT7n0aWrxiuf3ni/Df79ly2qAiNwoyauwrUmCpIJOTGjwKbUZbbi8dBbtnOzYeERHJcV6tnudKvaEAPBP1BdOmTtJy2CIit8nsCJmrsfYveZ0rWr8GDR4DDJg/GI6szvIpy9woyGilJZGCSwWZnNb8RbjnGcvt35+BI6scGo6IiOS8gG4fcr5Sb1xMZgaeeoe5f/zu6JBERPKUzDb1vRaXuYa+Oc5kgi6fQPVukBQPv/aH8/9l6ZQaISNS8Kkgk9NMJujwIdTsCeZE+HVAlpOziIjkcSYTJR+ZzOnizfE0xdNmx3Os2fSPo6MSEckzMtvUNzouAciDBRkAJ2fo9T2ENIW4KPi5N0SezvTpbAUZ9ZARKbBUkMkNTk7QY9LN5DzjwSwlZxERyQecXQh68hdOe1alqOkqIYsHEnbkqKOjEhHJE25OWbLvuOgbI2TsXWEp17i4w8MzoFhVuHrG8ro/NjJTp7I19Y24rqmvIgWUCjK5xdUDHvoZilWBqNMwsw/ERjk6KhERyUnuPpR8+g8uOpckxHSO+Ol9uByRuRfmIiIFSWanLEXH3hgh45FHCzIAngHQfy74lIQL/1lGyCcl2H2a0v6emEwQl2gm/Fp8DgQqIo6mgkxu8gqEfnPBuwSc3wPznoCkREdHJSIiOcjFvzTug+YThQ+1jDD2fzOAxETlfhEp3DI/ZelGU1+3PFyQAShSDh6ZDa7ecHS1ZfUlO4tPbi5OFPdxBzRtSaSgUkEmtwWEQN9fwMUDDv4Ff73u6IhERCSH+QXXIrLbDyQYzjSJXc2GH15ydEgiIg7llNkRMtamvnl5hIxVmbrQ+wfABNunwcaJdp/i1mlLIlLwqCDjCGUbwAOTLbf/+Qb++dax8YiISI4Lrt+R/Xe/C0CLs1PY8vtXDo5IRMRxnG+8C7F32WtrU98820PmdlU7WRb4APhrNOxbaNfhauwrUrA5tCATm5DkyMs7Vs0e0PYty+0lI+HQcoeGIyIiOa9212FsDnoUgDo7RnN4q3K/iBRON5v6Zm7Za9/8UpABuPcZaPgEYMD8wXB2V4YP1QgZkYLNoQWZTp+v4fu1R4iJL6Rz6Zu9AHX7gWGGOY/DpYOOjkhERHJYw8c/Y5tXM9xMSQQsfJyIs0ccHZKISK5zyWRB5mqs5X1DvhkhA2AyQaexUKkNJMTArEcg+kKGDi1bRAUZkYLMoQWZi9HxvP/nPpqPWcnXqw5xNdb+7uP5mskEXT+D4HsgLhJmPQzXIxwdlYiI5CAnZ2cqD5nBIafyBBJJxI+9SYqNdnRYIiK5yrrKktnOHjLXrE1980MPmVs5u0DvH6FoZYg6Bb/2h8S4dA+zjZDRlCWRAsmhBZm3769BuUAvwq/FM3bJAZp+vILPloUREVOIlnVzcbcsh+1XFsIPwdzHtfKSiEgB5+9fBPrOItzwo3zCYQ5+OwDMZkeHJSKSazI7Zcm2ypK7c7bHlOM8AyyLe7j7w8l/4M//S3flpaAiXoBGyIgUVA4tyPRuGMyKF1vy2UN1qFTcm6jYRCb8fZBmY1YyZsl+LkWnXzUuEHxKQN9Z4OoFh/+G5W85OiIREclhlUNrsK/lJOINZ6pdXsHBecr9IlJ4ZHmEjLtrtseUK4qFwoM/gskJdvwM/0y+4+5lingAEHk9wVaMEpGCw+GrLLk4O/FAvbL89UJLJj5Sj2qlfImOS2TSqsM0G7OCd/+3l3ORsY4OM+eVvgt6TLLc3jgRds9xbDwiIpLjmrXpypLyIwGotOdLzm/5zcERiYjkjsyOkLkaZ+0hkw9HyFhVbgft37PcXvoaHF2b5q6+Hq743ZiepWlLIgWPwwsyVs5OJrreVYbFzzfn+4ENqVPWn9gEMz+uP0qLsSt54/d/OXUlxtFh5qyaPaD5i5bbC4bZ1YFdRETyp04DX2aJZ1ecTAY+fw4l9ux+R4ckIpLjnG0FGfuOs46Q8c2vI2SsGj8LtfuAkQRzHoWIE2nuGhRgnbZUwN8LiRRCeaYgY2UymWhXoyS/P9uUnx5vxN3lA4hPMvPzphO0GreKl+fs4uila44OM+e0fh0qt4fEWPilP1wLd3REIiKSg1ydnag7eBLbqY43MUROeRAjNtLRYYmI5KjMTFlKMhvExFuWvc7XI2TAsrjH/ROg1F0QE25p8puQ+giYINtKS4Vg1oBIIZPnCjJWJpOJFlWKM+fpJvzy1L00q1yMRLPBnG2naPvJKp7/ZQdh5686Oszs5+QMvb6HwIoQeQLmDlKTXxGRAq5UoB9JvadyxgikZPwJTk95VE1+RaRAy8yUpWvxN18T57tVllLj5gUPzwCvopaR8f8bkWqT37JaaUmkwMqzBZlb3VuxKD8/eQ/zhzahbbUSmA34Y+cZ7vtsDU9P38ae0wXsk0TPIvDwTHD1hqNrYMV7jo5IRERy2N21qrG+/ufEGS6UPb+S84s/cnRIIiI5xtlSjyHJjhEy0bGWgoyrswl3l3w+QsaqSDl4cCqYnGH3L7Dl+xS73Bwho4KMSEGTLwoyVvXLBfDDoLtZ+FwzOtUqBcCS/87R9ct1PDZlM9uOX3FwhNmoRHXoPtFye/3nsHeBQ8MREZGc1+v+bswsNhyAYlvGE7NvmYMjEhHJGdYeMmZ7RsjYVlgqAKNjblWhBbR723J7ySg4uTnZ3UG2ETLqISNS0OSrgoxVrSB/JvVvwF8vtKB73TI4mWDlgYv0mrSBft9vYuPhcAw7l9DLk2r1hMbDLLd/HwoXwxwbj4iI5CgnJxM9Hh/F/5zb4YwZ85zHMa4cd3RYIiLZLjNTlm6usFTACjIATZ6DGt3BnACzB0L0BdtdGiEjUnDly4KMVZWSvkx4uB4rXmxFn4ZlcXEysf5QOH2/20SfyRtZHXYx/xdm2r0DIc0g/irMHgBx0Y6OSEREclCAtxtl+03kX3MFfMxRhE/pC4lxjg5LRCRbZaapb4EdIQOWJr/dv4JiVeHqWZj7uK2PpHWEzIWrccQnqr+YSEGSrwsyVuWLeTO2dx1WvdyKAfeG4ObsxJZjV3j0x830+Go9y/aez7+FGWcXeHAK+JSCi/th4QupNvsSEZGCo17F0uxt/hVXDB+KRf1H+PyXHB2SiEi2yswIGWsPmQJZkAFw94WHfgY3Hzi2FlZ+AEBRbzfcXZwwDDgbqVEyIgVJgSjIWJUN8OK9HrVYO7I1TzSrgIerE7tORTL4p610mrCWhbvP2JX08wyfEpaijMkZ/p0NW390dEQiIpLD+rRrwvTSrwFQdO9PXN82y8ERiYhkH+sImSQ7XppHW0fIFIQVltJSvAp0+8Jye92ncGAJJpNJ05ZECqgCVZCxKunnweiuNVg3sg1DW1XCx92F/eeuMmzmDtp/tpp5206RkJTPhvuFNLml2dercHq7Q8MREZGcZTKZeHTgU0x1eRAAp4UjMC7sd3BUIiLZIzNNfaML8pSlW9XqBY2GWG7/NgSuHL+lsa8KMiIFSYEsyFgV83HnlY7VWD+yDSPaheLv6cqRi9d4cc4u2nyyipn/nCAuMcnRYWZck+egWldIiofZj8L1ArSqlIiIpODv5Uqd/h+zwVwTdyOWyGl9If6ao8MSEcky65SlRHPGPyQt8FOWbnXf+xDUEGIjYM6jlPOzLPOtETIiBUuBLshY+Xu5MqJdFdaNbM3IjtUo6u3GycvXee23f2k1bhVT1x8lNiEfFGaszb4CKkDkCfj9WfWTEREp4OqVL8aRll9wzgigyLUjRMx5TrlfRPI9W1NfOwatR8cXooKMixs8OBU8A+DMDvpc+RbQCBmRgqZQFGSsfD1ceaZVJdaObM3orjUo4evO2chY3v7fXpqNWcm3aw7burfnWZ5FLMnZ2Q0O/AmbJjk6IhERyWH92jRgWunRJBkmihycR9zWnxwdkohIljjfeBeSZEeB2TpCpkAue52aIsHwwGQA6pz5lY5OmzVCRqSAKVQFGSsvNxeeaFaBNa+05r0etQgq4sml6Dg+XLSfZmNWMHHFQaJiExwdZtrK1IUOH1puL3sTTm1zaDgiIpKzTCYTgwcM4FuXvpbvF70M5/c6OCoRkcxzdrK8DbFnwQ3rB6e+Bbmp7+2qdICmzwMw1nUy5stHHRyQiGSnQlmQsfJwdWbAvSGserkVY3vfRfmiXlyJSWD8X2E0/XgFn/x1gCvX4h0dZurufhJq9ABzAswZBDGXHR2RiIjkoEBvNxr0e4/V5rtwM+KImt4P4qIdHZaISKZYR8iY7RkhE1fIRshYtRlNXOm78TNd5/VrYzHHxzo6IhHJJoW6IGPl6uxEn4bB/P1iKyY8XJfQEj5cjU3kyxWHaDpmBR8t2seFq3ks8ZlMliXxrP1kFqingIhIQdeoYjHCGn/COSMAv+gjRP02wtEhiYhkipN12WutspQ+Z1ecHvyRy4YPtZ2OELv4dUdHJCLZRAWZWzg7meheN4ilI1rwTf/61CjtR0x8EpPXHKH5mJW8veA/zkbmoXmbHv6WfjJOrrB/IWz+ztERiYhIDnu8w91MLvY6SYYJv/1zSNg+09EhiYjYzbrstQoyGeMaWI4PXYcD4LXje9j/p4MjEpHsoIJMKpycTHSsVZo/hzfjx0ENqRtchLhEM1M3HKPF2JWMmv8vJ8JjHB2mRZm6cN97ltt/vQ5ndzk0HBERyVnOTiaGDBzAt04PAmAs/D+4dNDBUYmI2Me2ypIdI7yvxVlWRfUpTD1kbnGiWAu+S+xs+eb3oRBx0rEBiUiWqSBzByaTiTbVSvLb0CbMePIe7qkQSEKSwazNJ2j9ySr+79edHLqQB+bv3/M0VO0MSfEw5zGIu+roiEREJAeV8vegSu932JBUAzfzda7+3B8S8tjUWhGRO3DKxAiZq9ZVltwKZ0GmbKAnYxMf5rxvTYiNgHlPQFIeXohERNKlgkwGmEwmmlYuxq9DGjN7SGOahxYjyWwwf8dp2n+2mmEzt7P/XJQjA4TuX4FfEFw+DH++6LhYREQkV7StWYaNdT/ikuGHb8R+ri0c5eiQREQyzDplyY56TOFcZekW5QK9SMCFaWXeBHc/OPkPrPrI0WGJSBaoIGOnRhUCmf7EPfzxbFPaVS+JYcDC3Wfp+PlaBv+0lV0nIxwTmFcg9PoBTE6w+1fYOcsxcYiISK4Z1r05X/haivDeu34kae//HByRiEjG2NvUNzHJzPUEy5SlQrfK0g3BAV4A7IwuAvdPsGxc+ykcWe24oEQkS1SQyaQ6wUX4/tGGLH6+OV3uKo3JBMv2nqf7V+t59MfNbD3mgGWoQxpDqxufkP75Ilw6lPsxiIhIrnF3cWbQo08yxegKQML8oRB5ysFRiYikz96mvtfik2y3vd2dcySmvK5cUUtB5uSVGKjVE+oPBAyY/xRcu+TY4EQkU1SQyaLqpf346pH6LHuhJT3rBeHsZGJ12EV6f7ORh7/dyIZDlzBycznq5i9C+eaQcA3mPQ6Jcbl3bRERyXUVi/vg2+U9dpkr4pEYxdVZj4E5Kf0DRUQcyN6mvtYVltycnXB3KZwFGesImTMRsSQmmaHjGChWFaLPWZr85uZ7DhHJFirIZJPKJXz49KG6rHixJX0bBePqbGLTkcs88v0/9Jq0gZX7L+ROYcbJGXp+C54BlhWXlr+T89cUERGH6nV3BX6v9C7Rhge+5zYTu+JjR4ckInJHTjfehWR4hIx1yetC2j8GoISvO24uTiSZDc5GxoKbF/T+EZzd4eBS+OcbR4coInZSQSabhRT15qOed7H65dYMalIedxcntp+I4LGpW+j65TqW7DmL2Z7uZZnhVwa6f225vekrOLg8Z68nIiIOZTKZeOGhjnzqNgQAt3XjMY5vdHBUIiJpu9nUN2Ovi20rLBXS6UpgWZmqbIAnACcux1g2lqoFHT6w3F72Jpz710HRiUhmqCCTQ8oU8eTtbjVZO7I1T7WoiJebM/+dieLpn7fTccIa/th52q5l/uxWrTM0espy+/enIfpCzl1LREQczs/DlS79X+C3pOY4YSbml8fheoSjwxIRSZWznU19Y+IL95LXVuUCb/SRsRZkAO5+Eqp2hqR4mPsExMekcbSI5DUqyOSwEr4evNa5OutGtmFY68r4ursQdj6a53/ZSbtPVzNn60kSksw5c/H270KJGnDtomVeqTmHriMiInlCg5AAzjd7j+PmEnhfP8O1+c+pp4CI5ElOdjb1vX6jqa+Ha+EdIQM3+8icvHJL0cVkgm4TwacUXDoAS19zUHQiYi8VZHJJoLcbL3WoyrpX2/Bi+yoU8XLl6KVrvDx3N63GreLnTceJS8zmJoyunpalsJ3d4dAy2Dw5e88vIiJ5zuD2dZlc/DUSDSe8Dy4gcccMR4ckIpKCvSNkYhMtHyx6uBbuty/WETInLl9Pfod3Ueg5GTDBtimw73+5H5yI2K1wZzQH8Pd05bm2oawf2YbXOlejmI87pyOu88bve2gxdiU/rDtq+wQgW5SsoXmlIiKFiLOTiWEDHuZr00MAmBe+BOGHHRyViEhytmWvMziKLy5BI2QAggMtPWSSTVmyqtgKmg633P5jGESezr3ARCRTVJBxEG93F55qUYl1I1vz9v01KOXnwfmoON5buJdmY1YwadVh2/J+WXb3k1Clk2Ve6bwnIeF6+seIiEi+VaaIJ6E932BjUg3czNe5OnMQJCU4OiwRERvrlKWMzqi3jZAppEteWwWn1kPmVq3fgDL1IDbC0kdSLQtE8jQVZBzMw9WZQU0rsPqVVnzUszbBgZ6EX4tnzJL9NP14BROWHyQyJosvok0m6D4RfErCxf3w1+jsCV5ERPKsTneVZXXNd4kwvPEN3831Ze87OiQRERvblCU7R8i4F/IpS9aCTPi1eNtS4Mm4uEHP78HVC46ugY1f5nKEImKPwp3R8hB3F2f6NirHyhdb8cmDdahY3JvI6wl8tjyMpmNWMHbJfsKj4zJ/Ae9i0OPGUthbvoMDS7IncBERybOG92zNBM9nAXDfNAHj2DoHRyQiYuFsZ1PfWOuUpUI+QsbPwxV/T1fgtsa+typWGTqNsdz++z04szN3ghMRu6kgk8e4ODvRq0FZlr3Qki/71qNqSV+i4xL5etVhmo1ZyfsL93IhKjZzJ6/cDu4darn9x7NaCltEpIDzcnOh14BhzDW3xAmDmF+egOtXHB2WiIitIANgzkBRJjZBTX2tbi59fYc2BPUGQPX7wZwA856A+Gu5FJ2I2EMZLY9ydjJxf50yLH6+OZMHNKB2kD/XE5L4ft1Rmo1dyZt/7OF0RCZ6wbR9C0rWgphLlqWwtRyqiEiBVivIn6utPuSouSTesee4Om+4cr+IOJx1yhJkbNpSrJr62lgb+55Iq48MWFoW3P8F+JaB8EOw9PVcik5E7KGCTB7n5GSiQ81SLBjWlKmP3U3DkADiE838tPE4LceuZOTc3Ry7ZEfF29UDen0PLh43lsL+LueCFxGRPOHRVjWZWup1Eg0nfA8tIGHHLEeHJCKFnNMt70IyMm0pNtHaQ0YFmXQb+1p5BcID32BbCnv/nzkfnIjYRQWZfMJkMtGqagnmPN2YWYPvpWnloiSaDX7depI2n6xixC87OHj+asZOVqI6tH/XcnvZaLiwL+cCFxERh3NyMvFs/4eY7NQHAPPCF+HKMccGJSKFWrIpSxkaIaMpS1bBARksyABUbAlNhlluL3gOrp7LwchExF7KaPmMyWSicaWizHjyXuY904TWVYtjNuD3nWe47/M1DJ2xjf/ORKZ/okZPWXrKJMZalsJOzELDYBERyfNK+HlQtddbbDFXwd0cQ+SMxyAplRU6RERygdOtU5YyMEImTste29h6yKTV1Pd2bUZDqdoQE25pWaClsEXyDBVk8rEGIQFMeawRC59rRseapTAMWPTvObp8sY4np21h58mItA82maD71+BVFM7vgb/fzbW4RUTEMdrVKsOamh9w1fDE/9J2rq0Y6+iQRKSQSt7UN/391UPmpuBbmvoaGekJ5uJuWQrbxQMO/w2bv83hCEUko1SQKQBqBfnzzYAGLB3Rgm51yuBkguX7LtDjq/UM+OEf/jkSnvqBviWh20TL7Y0T4ciqXItZREQc49mebfna82kAPNaPwzi11cERiUhhlPmmvnr7ElTEE5MJrickcSk6PmMHlagG7d+z3F72ploWiOQRymgFSNVSvnzRtx7L/68lvRuUxdnJxNqDl3jo2030mbyRtQcvpqyiV+sMDQZZbv/2DMRczvW4RUQk93i4OtNt4Av8aW6MM2auznwM4qIdHZaIFDJOTnZOWbrRQ8ZdU5Zwc3GitJ8HkM5KS7drNBgqt4ekOLUsEMkjVJApgCoW92H8g3VY9VIrHrmnHG7OTmw+epkBP2ymx9cbWL73fPLCTIcPoWhluHoGFr6g5VBFRAq46mX8iWgzhtNGUfxiThDx+8uODklECiHrtKUMNfVN1AiZW1mnLZ3KaB8ZuNGy4KubLQtWvJdD0YlIRimjFWDBgV58+EBtVr/SikFNyuPu4sSukxE8+dNWOn+xjkX/nsVsNsDNG3p+B04usPd32PWLo0MXEZEc9kjLu5he6lXMhoki+2YSv2eBo0MSKZCi49Q8Oy3WaUsZWvZaPWSSsRZkToTbUZCB5C0LNkyEI6uzOTIRsYcKMoVAaX9P3u5Wk3Uj2/B0y0p4uzmz72wUQ2ds577P1/DbjlMklqoLrV61HLDoZS2HKiJSwJlMJp4c8Cg/O3UDIOG3YVoOVSSb7T4VQdtPVjk6jDzL6cY7kYwVZLTs9a0qFPMG4Oila/YfbGtZYMBvT8P1K9kam4hknDJaIVLc151XO1Vj/atteL5tKH4eLhy6EM0Lv+6i7aerme3RG3PZeyD+KswfouVQRUQKuGI+7oQ8+AH/mUPwTookfOaTmrYqko0+WxbGtbgkR4eRZ2VmhIx6yFhUvFGQOZyZggxYWhYEVlLLAhEHU0GmECri5cYL7auw7tU2vNyhKoHebhwPj+GV+Xt58MIg4p294eQmWP+Zo0MVEZEc1rJGMGtqf0Ss4UrRs2u5uuZrR4ckUiBsP3GFlQcuJlveWZKzNvbNyCpLcYnWETIqyIClZyTAkQvRGVv6+nZu3tDrOzA5w3+/we5fszlCEckIuwsyjz76KGvWrMmJWCSX+Xm48mzryqwb2Zo3ulSnuK8726L8GXl9IADmlR8Te2yzg6MUKUDy8Txt5f6C7fEHOjLF63EA3Fe9jfm8lkMVyarPloUB8EKlMw6OJPNyOvfbmvra1UNGnycDhBT1wskEV+MSuRidydWSghpAq1GW23++BFeOZ1+AIoWZYcDhVRna1e6MFhkZSbt27QgNDeXDDz/k9OnT9p5C8hgvNxeebF6Rta+05r3uNfnHpx0Lk+7FyUjk/NSBTF7+L1GxCY4OUyR/C1sKv/ZzdBSZptxfsLm7ONPu0TdYa9TBzYjn8vRHtRyqSBZsOXaZtQcv8YDLBgadfMPR4WRaTud+25SldEZ4GIahETK38XB1pmyApbHvkYuZnLYE0OwFCLa2LHgKzJpiJ5JlW3+E2f0ztKvdBZnff/+d06dP88wzz/Drr79Svnx5OnXqxNy5c0lI0Jv2/MzD1ZkBjcuz6pU2xHcazwVTUUI4i8+qt2j68Qo+/esAETHxjg5TJP+Jvgh/POvoKLJEub/gCy3lx4U2n3LZ8KFY9AEuLnjT0SGJ5Fuf/hVGGS7xodtUR4eSJTmd+21TltIZIWMtxgC4u2iEjFXF4pY+MlkqyDi7QM9vwc3X0rJgnVoWiGTJpYOw9PUM756pjFa8eHH+7//+j127dvHPP/9QuXJlBgwYQJkyZXjhhRc4ePBgZk4reYSbixM9m9SmaL8fAejn8jeN4v/hixWHaPrxCj5avI9LmR0aKVLYGAYsGAbXLkKxqo6OJkuU+wu+ni0a8GuplwEounsy18NWOTYgkXxow+FL/HPkIp+5TcLTHA2l6zk6pCzJydzvYpuydOf9rNOVQCNkblWx2I0+Mhejs3aigPLQeazl9qqP4PT2rJ1PpLBKjId5T0LidSjfLEOHZKnEfPbsWZYtW8ayZctwdnamc+fO/Pvvv9SoUYPPPlN1Nb9zrtwKGg8D4GvfKTQumcS1+CQmrz5CszEreOd//3EuMtaxQYrkMWFhsHgx2F6fbpsCYUvA2Q26T3RobNlFub/gMplMPDxwKAuc2uKEQeycwXA9wtFhieR51twfFmbw6V9hDHb+k3uc9oGrN3Sb4OjwskVO5H6nDE5Zsi557exkwtVZI2SsKpW4sdJSVgsyAHX6Qo3uYE6E+YMhPgujbkQKiRSv+1d/DGd3gmcAdPk8Q+ewO6MlJCQwb948unbtSkhICHPmzGHEiBGcOXOGadOmsXz5cmbPns27775r76klL2r7JpSoiXvcZWaW+JkfBjagTnARYhPMTFl/jBZjV/L6b/9y8nKMoyMVcajLl6FjJ4OqVaFzZ6hSBZ544CDGktcsO7R7G0pUd2iMWaHcX3gEeLtRss/nHDNKEpBwgdMzhjo6JJE86/bcX6fTRa6f2MGLLrMtO3QaA4EVHRtkFuR07nfO4JQlW0NfTVdKxjZCJrNLX9/KZIKun4NvaQg/BH/l395HIjkttdf9Lz64AcM65a/r5+BXKkPncrH34qVLl8ZsNtO3b182b95M3bp1U+zTunVrihQpYu+pJS9ycbcsifdta0wHl9K2ykLaDH2C9YfC+WLFQTYfvcyMf07wy5aTPFAviKGtKtmW4RMpTB7pZ7BiTSJFu+7BI/gyiSf9eKbES5gSr0OFlnDPMxCdDZ9gOYhyf+FyT7VyzKj9IWX/HUzQqT8J3/gzRRtnrDmdSGGSPPeH4+kaw+euX+FmSoJqXaFef7h61dFhZlpO537bKkvpjZBJtK6wpOlKt6p0o4fMycsxxCUm4e6SxZ+PVyD0mATTe1iakoZ2gKodsx6oSAFz++t+19NuPFf2GUyGGer2g5o9ICoqQ+eyu8z82WefcebMGb766qtUkzJAkSJFOHr0qL2nlryqZE3Lp/sAS9/AdOkgzUKLMXtIY3596l6ahxYjyWwwd9sp2n26mudm7eDAufz74kPEXmFhsHSJCb82e/CpeQYXv1herzORhqV3cvl6EY7WnQRO+ftTPeX+wqfPAz2Z49MXAI+/XiEx/JhjAxLJY1Lm/jhe951OqNNpzkaX4HDNLyyjDvKxnM79N+oxGRghoxWWUlPc1x0fdxfMBpwIz6bR6pVaw703FiL441mIvpA95xUpIFJ73T/+ro8p73+SI1dCOFzlY7vOZ/c7hAEDBuDh4WHvYZLf3fM0VGxlaVA0/0lLwyLgnopFmf7EPfw2tAntqpfAbMD/dp2hw+drGDJ9K3tORzo2bpFccPiw5V+P4MsANDTtZ6jzHwAMWfg5+88EOSq0bKPcX/i4OjvR7LGP2WWE4m1c49y0QVoOVeQWt+f+Vk47GeTyFwCDfp9E2Kmijgot2+R07reNkElvlaUbU5bcXfP3hxvZzWQy2UbJZEsfGasbLQuIuQR/DLMsUCAiwK25PxyArk4b6eW8jiTDiQG/fUvYcT+7zqesJhnj5AQ9vrE0KDq7C1Z9mOzueuUC+P7Ru/lzeDO61C6NyQRL/ztP1y/X8diUzWw7fsVBgYvkvEqVLP/GngzElxg+d/saZ5PBrEsdmbv3ASpXdmx8IpkVXMyPS/dN5JrhTtmoHRz/30eODkkkz7g19xclknGukwGYfKEnfx1up9yfARlu6ntj2WuPrE7JKYCsrQIOZ2Xp69u5elhaFji7wcGlsPWH7Du3SD5nzf1JMe6UJpwPXC3/Pz47258NJ++1O/erICMZ51ca7r+xUsC6z+HYuhS71Czjz1f96rPshRY8UC8IJxOsPHCRXpM28Mh3m9hw+BKGquxSwFSpAh06GkStqMUb12ZT1nSJY3GlGTZjEh06GoSGOjpCkcxr2/Re/gwaAUDQjk+JOrzFsQGJ5BG23L+6Gh85/0BxUyT740N4ecYE5f4Msrupr0bIpFCxmGWEzJHsLMhAipYFXAzL3vOL5FNVqsB9Hc24esTyiesk/E0xbI8P5c1ZYzKV+5XVxD41ukPd/oAB84ekuRxq5RK+fPZQXVa82IqHGgbj4mRiw+FwHvnuHx78ZiOrDlxQYUYKlFkzTbzT4w8eKvoXSWYn+s2Yyt33BjBrZv7uHyAC0GXgy6xxbowLSVz75TEMLYcqAlhy/9sDvuA+163EGS48NHU6TZr4KvdnUIab+lqnLGmETArWETJHLuXAwgH3PJNqywKRwu659y/xTNF5NHHeS4zhznPhL9KimWemcr8KMmK/Th9DQAWIOgV/vnjHXcsX82ZM77tY/UprBjYOwc3Fia3HrzBoyha6f7Wev/47l+68YZH8IMB0klG1/g+Ao8EvMfXve1my2ERAgIMDE8kG3h6uFH/kG84bAZROOEnYT887OiSRPMElei8vFB8PwMrAF5i7uo5yvx1sU5bMd94vztbUV29dblepxI0eMheis//DzttbFqz8IHvPL5JPbdu6nBddZgPwTuJAzgT4Mee3xEzlfmU1sZ+7L/T8DkzOsGcu7J6d7iFBRTx5t3st1r3SmsHNK+Dp6szuU5E8NX0bnb9Yy/92nUl3uKpInmVOgt+GQFwk/H979x1Xdd3+cfx1BnspKA4EF4p75540HNk0KzUz26XtXXd39etul+0yK7M0La1smCMT98y9xS3uAcgeh3N+f3wBIUFAgQOc9/PxuB/CmZ/DHRff7/W9rusT0onwO59WqbpUOc0bN2BDR2OGTMThGRxc+ZOTVyTiZLYMkqbdgRcZbLC05cqxzyn2l1CxW5a07XWhGgT5YDJBQpqNM8llUMHiXweu/dj4evmHsH9p6b+HSCVy+MRpbjvyf7ibskhuNJDlfgNxAJsPX9xmNkrIyMUJvQz6PGN8/ecTEHewWE8L9vfkhatbsPzZSMb0a4yvh5WdxxN5aNoGrhy3mJ/WHSazqMskIhXN8g/h4HJw84EbJ4DFzdkrEikT/a+5lb/8bwLA/6/HSY496uQViThP4tz/o07KLuIcviRf/TEWi5IFJWUxlaxlSQmZ83m6WQip5gWUwRyZHM2vgfYjAQfMvB9StVmHuK6TPz9NY/Mx4syB+Nz0Ge3rBwKw4dDF/V4oISMXr9cTENoF0hPgl3shy1bspwb6uPNU/2YsfyaSx69sSoCXG/tOJ/PkjE1EvreIqasPkW7T9qpSCRxZf66Ed9DbENTYuesRKUMmk4nL7vqA3ab6VHec5dDXd2g7VHFN+5fis/YTACZWf5Qe7ds4eUGVkzn7TMRW5FBftSxdSO4cmdLc+vrfBrwJgY2MkQWzHlPsF5eUse1POpz8GYC9Pd8F70DahVYDYGNM/EW9pqKaXDyL1agGcPeDmFWwbFyJXyLA242HL2/C8mcjeXZgM2r4uhMTm8rzM7fQ5+1FfLN8P6kZSsxIBZWRDD/fDXYbNL8W2o1w9opEylz1AD9Sr/mCNIcbzZNXs+nnt5y9JJHylRpH5k/3YMbBj7a+RN54NyaThvhejNyhvkUkZHIu0mmob8Ea18zeael0GQ5c9/CFIV+B2QrbZsKmaWX3XiIVUeIJ+H0MAFPNg2nX5wYA2odVA2DDofiLmuOkhIxcmuoN4Or3jK8XvQkxF7cdqq+Hlfv7NGbp05G8dE0Lavt7cjwhjVf+2E6vt6P4YvFektKLX4EjUi7mPguxe8E/xNgSXgfk4iLadOjGysaPAdBsy7vE7NRW2OIiHA4cfzyKW/Ix9tlrszriadqHaYLvxTo31Le4FTJKyBQkp0Jmz8kyrJABCOkIfZ8zvp79FMTuK9v3E6ko7Hb49QHc0+PYbq/PjpaPY7UYqZSWdf1xt5g5k5xBTGxqiV9aCRm5dG1vgdZDwZFlbImXlnDRL+XlbmF0j4Ysfrov/7u+FfWqe3E6KYM35uyk51tRfLRgN2dTM0tx8SIXafvvsP47wAQ3fAHegc5ekUi56j3iOdZ5dMHDlIlt+l2kpZTxiYBIRbBxKqbtv5LpsPCU/SEeHdTe2Suq1HKH+hZ7hoxOXQrSrLYfADuOXfwxeLH1fAzq94SMJPj5HsjScbm4gDVfwN4FpOPOw5lj6N28Xu5dHlYLzev6A7AhpuRzZBTVpHRc/R5UC4O4AzDn6RI9NToa5syB3bvP3eZhtXBb1/osfLIv79zUhkY1fIhPyWTc/Gh6vhnFu/N2EVsWk+RFiiPhKPzxsPF1z0ehYS+nLkfEGSwWM6Gjv+Y01WhoP8iGiSXbCrug2C9SoZ3ZiyP7GGecbSgdu19OWJC3kxdVueUO9S1mhYxalgrWvI4/JhMcO5vG6aT0sn0zswVu/AI8A+DIWlhcsrZVxX6pdI5vhfn/BeDVzBEcMofRvXFQvoe0z54js+FQfIlfXgkZKR2eAdlbYZuNntLNM4p8SmwsDBjoICICBg2Cpk2N7+PyJBbdLGaGdgpl/uN9+GhYe5rW8iUx3cYnC/fQ480oXvtzOycT08rwg4n8iz3LGGKdGgd120Pf5529IhGnCa4dytG+xvywbqd/4p+/ip4pUJzYL1Lh2DLg57swZSSxMqsF092vZ0y/cGevqtIzF7dCxqYKmQvx9bDSsIYxR2bb0XKokgmoZ7RqAyx5Fw4sK/Ipiv1SKWWkwM93QVYGB2v0ZkrWFXRpFIiPhzXfw3LmyFzMYF9FNSk9YV3zbIX9uFEtcwHDRziIWmIjaPAGQh5YQNDgDUQtsTFs+Pl/lC1mE9e2rcvcR3oz/raOtArxJzUziy+X7qfnWwt56betHI0vec+eSIkt/wAOLDW2uB7yNVjdnb0iEadq03cI/9QeBkDj5U9x+NCFZwqUJPaLVBgLX4OjGziLL49lPsBDVzQjwMvN2auq9KzFHeqrba+L1KpuAABbj5wtnzdseQO0vw1wnLtQlc3hcJCQlklSuo2UDBu2LLtiv1ROf70Ap3aCb21et44FTPSLCD7vYe1DjVli248mlHinYGvRDxEpgV5Pwt6FELOK1Cl3s7jRHBo3daNJk/wPi46GeXNNBA3eim/LowDZ/5qYN6sdu3dz3nPAuJIyoFVt+resxaLoU3y8YDfrD8Xz7cqDTF1ziCEd6vFg33CVEEvZOLwWonK2uH5HW1yLZGs/+n32v7OahrZ97Jt0J+s7zKd5ROnFfhGn2rcIlhvVAE9n3I13jTBGdK3v3DVVEbkVMtr2+pK1CvHn901Hyy8hAzDgLTi4EmL3kjj1YZbV+Q5rjSQ+XL2RrUfOVep4WC0cO9MU/8h4fFseAxT7pRLY8QesnQhAyuBPiZpsjMvo1+z8hExooBdBPu6cSc5g29EEOpRg2LuimpQui5X4y78kyeaP15l/+Oe9twosSdy71/jXMzQ239M9Q88AsGfPhd/GZDKykz8/0J2pd3eha6NAMrMc/PBPDP3eW8TjP24s+0nz4lrSEoySRUcWtLwR2g1XH7RINquHF1mDJ5HqcKeTfQP/zHi5TGK/SLlLPgO/3Ac4+CHrcubZO3NHu+b8/ZdZsb8U5MyQySqiSCJ3qK9myBSqVUh2hczRckzIePhy9qqvybS74RfzO39OeJ+7flyWLxkDxrblgZE78G56It/tiv1SYZ09Ar8/ZHzd/WGW2FqSmeUg2MsHW5zPeQ83mUy0yB7sW9JzUCVkpNTd+kAo9842Zgq80Otdrr114nkliY2zCwvSYvLvTJO8oy4A1mLWbplMJrqH1+CHe7vx0/3d6NO0Jll2B79sOMKV7y9mzPfry2fivFR9s5802vACwojr+T4DBqE+aJE8xj7XhqfXvQDAiw0+58rRk8os9ouUC4cDfhsDScc55hbGy5m34ZNQg1FXBiv2lxJLMVuWzs2QUUKmMC2zW5ZiYlM5m1J+Ox/d8lg7XlxqbIX9Tts3aOIeQ9rBIBpv78fOVwew/f/683D3VjhsZsxu9nzPVeyXCsmeBTPvM9rw6rQjtv2LPPPhSQD2LK1ZaOz39zTaWHMSyMWlhIyUqpxy9L9CwvnR1hezycH4pq9S/8oVzJtryr2a1LQp9B/gICGqFUnbQsg46cvRb3oSv6g5AFddVfKDnE4NAvn2zs78PrYHV7aohcMBf245xsAPl3L3t2vZdBFDlkQAjs2dBpt/xGGywJAvGXZngPqgRfLIif3TTL2ZndUZd1MWX9R7nbqDVpZ57BcpKydnTYDoOWSZ3Lgr6X7SHJ7s/70pQYM3KvaXErOpeEN903N2WVLLUqECvNwICzRa9reVU5VMTuyf3Lg9S7Na4WXK4BO3j7EkQ9Qf3sQcsODtbuXxa+vTcG93bHHG+hxZJo5N6arYLxXS6V/HwYGl2K3GvMhht1uJ9TgFgE/zI4XG/pyEcUqGEjLiRHnL0V+23c5eex3qmGL5pPmrgCNfSeK0qSYie1s5M6sdxyb1xnbWu1ROcNvUq8aXt3diziO9GNymDiYT/L3jBNd9upzbJ67hnwOxRb+ICMaOAHfdsBu/JU8A8OKC5+h1WxfmzTXhH2nMwLD6p+Hb8ij+kdvynXiKuJJzsT+OZzPv5rCjBg3NJ3iv6duYrFnlEvtFSktsLDwwZDMBq/8DwEuxo9nuaEDC2gZ4tz+g2F+KLNlnIkXOkFGFTLG0CjFaJsqrbWnvXvBqfAK3Gqk8nvkApx3+NDcf4n/NPgDytyLNnBhA88M9sMV7YbI48OtwULFfKpTYWHh86EqqbXwDgDtmvEevGxuzcH0iFl9jO3mLT2ahsd/b3YhPqUrIiDPlLUdPxZOHMh8i3WGlv8c/jLnsS8Lz7BBZvTrMnWNi3jzAYSLwytI9wW1ex59Phnfg78f7cGOHECxmE0uiTzF0/Epu+WIly3afxlHEFRlxbaNuS2NMrTvxdU9mRUYrJgT0Y+Wa7INCzcAQyZU39ifgyyMZY8hymBjitpT7bnmvXGO/yKUaPTKJR+uOxsOawfyMjkzx6kNWihtnlzdR7C9lxW5ZyhnqqxkyF5TTtrTlSPm06/vVSiXo6k0AnKI6T2Q+AMBo7zlc03T2ebF//p/uPBfZDocdfFscU+yXCuXe2+N4pN7dWM1Z/JzWh9lhzVi5JguflkfOe2xBsd8rOyGjliVxqn+Xo28+24yXY4zgPG7Af2jit+W852Rl/zdbVgc5jWv6Mu7mdix8oi/DOofhZjGxen8st329mhs+W0HUzhNKzMh5oqOhb9ardKi9mTiHL4/Z78e75Qn8uhlHCv+egZEWEwSQ7+BDxFX8O/avPtuWd06PBOCdxu+x7+jy855T1rFf5GJER8M1lmeJCNrDcUd1nrbfA5jIOBGAPd1Nsb+UFbdlKecERy1LF5Yz2HdbOey0lJllZ9yq9Vi8Msk44U/S9rosiO/Cp8dvAWDKTQ/SJPj8E9lGfoEkrDr/F0axX5wpepeDW7weoX7AYQ7Ya/ESI/FteRS/7rvwbX34vMcXFPvVsiQVRt5y9COfX86b37zKqrj+uJvTYcZoSM8/ebqwIY+lfZATFuTNGze2ZsnT/bijewM8rGY2xsRz56S1DP54GXO2HCvyCo24joS1c3mi2ycAPJV5Hycw/vv0aX4UTA7OLjBOPG0JniRtCyEhqiX9Bzi0baO4rH/H/hc+/4B1aR3wNaVRL+pBdh05le/x5RX7RUoiZfUM7u4wGbvDxGOZDxKH0QLiFpSo2F8Gilshk5677bUqZC6kVfYuL/tOJ5OYVraDfb9dcYD1h+Lx9bDSLLYDZ/5oz5HPL+exLz8hOqkd/m5x8PPdkGXL97zGjSF+eROyUt3y3a7YL86UsXIiQ1v+RobDysOZY0nCmHfk2/oIFq/M7Jhf94KxP7dlSRUy4mw55ejR0TB7NkRHm+j6+ufgVxfO7DZ2q8nj31dWy/ogp06AFy9f25Jlz0RyX59GeLtb2HY0gQe+X0//D5bw28Yj2LLsRb+QVF1nj9D+wP0AjD8xhL/tHXPvSosJAoeJbpedO/E8M6sdkb2tTJtqctaKRZzu37F/5y4L7Z+dQoI5gJamA2yb9AgJeU4Qyjv2ixTpzF7aHHwUgHGnh7PS3jL3rrSYGor9ZaA4FTJZdgcZWTktSzp1uZAgXw/qBngCsONYYpm9T1xyBh8tMCqG/zu4BVG/+eTG/m073Wn6/Dfg7geHVsDiN/M9t2lT6H+VidM/dSbn//aU/TUU+8V5jm+hxSFjp7BXD9/LZkfjc/dl/zcaFB/GmVntLxj7vdyUkJEKpkkTGDjQ+BefILjpazCZYdM02Dgt32P/fWW1PA5yavp58NzA5ix/JpKHI8Px87Sy+2QSj/ywkSvGLWb6PzFk2JSYcTlZNvj5biwZcexObsuT339U4MniksV5k47GiWj16s5evIjz5Y395mohmG74HIAbM//k+0mf5WsRdUbsFymQLR1+Go3ZlsTmhO58lDYUAHuGRbG/DOVUyFzoOli67dzJjSpkitYyu21paxm2LX24YDcJaTaa1/FnSMd6wL+O+wMbwTUfGA9e8i7sW5Tv+dOmmujTJoCkTWEAmM0OxX5xjvQkmDEasz2d1XH9eeuHV3KP+1P21sTinQkOE/O/CC0y9ucmZNSyJBVW/e7Q18g+8ucTcCo6967zq2rK7yCnuo87j18VwfJnI3nyqqZU93bjwJkUnv55M/3eXcTkVQdLPJxJKrHFbxlXdNz9CH7wG3r28Cn0ZDHfwYeIFMiv9dWcbHUPAMOPvckPf52bJ+PM2C+Sz/z/wrFN4BXIhstfwlwzhaxUN46Mj1TsL0PnEjKFZ2RyBvqCEjLF0Sp7sG9Z7bS071QSU1YdBOA/VzfP/f/wPK1vgg63Aw745V5IOpl7V07s//2NcCwmE571z/DSJ7GK/VL+Zj9ldHD41SXimc+J7O2We9yflegFwFXNaxPs51lk7PfSLktSKfR6Ahr2hsxkmHEHZKbmu9uZBzn+nm6MjWzCsmcieX5QM2r4enAkPpUXf91Kn3cW8vWy/SX+BZNKZu9CWPKO8fU1HxDQsLFOFkVKQfD1r3M6oBUBphQilj/Kqt3H892vE1xxqh1/wOrxAMT1/4h31hgnso9dHsGsn90V+8tQbstSMSpk3Cymwk/+JVfu1tdlVCHzxpyd2OwOLm8WTI/wGhd+8IC3oGZzSDoBv9wD9vzH0T3aezGsSygA7/8drU02pHxt+B42TTU6OIZ8RbW6QbnH/T//nknNTsZQ6tG96hfr5dSyJJWD2QI3fgk+NeHkNpjzjLNXdB4fDyv39m7Msmf68cq1LakT4MmJhHRenbWdnm9F8dmiPWU+KE2cIPG4cbCAw7ii0/qm3Lt0sihyiazuBI2aQqrZlw7m3URPfYpjZ1OLfp5IWYs7AL+OMb7uNpYXttUlKd1Gu9BqPDI4TLG/jFmyz0TsFzgR15bXJdO6nlEhs/tkErHJGaX62iv3nmH+9hNYzCaeG9S86Ce4e8PQSeDmbbQtLR133kPG9AvH3WJmzf5YVu49U6rrFSnUyR1GxwYYHRwNeuTe1aQJxFaLIc2WRXiwL10bBRbyIvmpQkYqD7/aRlIGE6z/FjZPd/aKCuTpZmFU9wYsfqofb9zYmrBAb84kZ/D23F30eDOK9+dHE59Sun/oxEmy58aQfAqCW8LAt529IpEqxxTYEPMNnwFwu+N3Jk78XHO6xLls6Ua1bvpZqHcZC0MfYPaW41jMJl6/obWqMcqBJbdC5kIJmZwtr5WQKY5gP0+a1fbD4YClu08V/YRicjgcvDNvJwAjuoQRHuxbzAU1g6vfM75e9DrsX5Lv7joBXgzrbFTJjJuvKhkpBxnZnRq2VGjUz+jgyGNTTDxvz9sFwKjuDTCZive3wEu7LEml0rgf9Hna+PqPR/PNk6lo3K1mhnUOI+qJPrx/S1sa1/QhIc3Ghwt20/Othbw1dyenk9KdvUy5FIvfggNLwc0Hbv4W3LycvSKRKsmj9XUktL0bgDHx7/LRLwucvCJxafP/C0c3gGc1Uq/7iv/8bhyL3NWzIS2ytw+WsmXOmSFzwQqZ7ISMdlgqtj4RNQFYHF16CZnF0adYfygeTzczYyNLuDd1u+HQbgQ47MYFsDzzZAAe7BeOu9XM2oNxrD8UX2prFinQn0/CqZ3gm10kYD6X7D2ZmMZ9k9eRYbNzRfNgRnQOK/bLqmVJKp8+z0CDXtnzZEZBRoqzV3RBVouZG9rX46/H+vDp8A40q+1HUrqNzxftpedbUfzfH9s5kZDm7GXKv0RHw5w5sHt3IQ/YsyDP3JgPoYZq00XKkv81b5AQ2IZqpmSu2PoMM1bvdfaSpAoqMvZv/y13bgw3fMEH/6RyJD6VkGpePHqF/g6Ul5wKGfsFK2SyW5bcdNpSXH2aGgmZJdGnLvizLS6Hw8H7842E5ciu9Qn28yz5iwx6B2o2M+bJ/HxXvnkytfw9ubZtXQC+W3ngktcrrqvI2L9+8rm5MTd9Db41c+/KsNl5cMp6jiekER7sy/u3tMtNGheHdlmSysdsgSFfg08wnNwOfz4OlaBM0WI2cXWbOsx+uBcTRnakTb0A0jLtTFy+n15vLeQ/v27hcFzFTi65gthYGDDQQUQEDBoETZsa38fF5XnQ2cPGlRoc0PEOaDPUSasVcSFWd/xHTiHN6kc7815SZj3PhkNxRT9PpBiKFfvP7D03N6b7w2z17cZXy/YD8H/XtcTb3Vr+C3dRuRUyF0rIZA/11Q5LxdepfiA+7hZOJ2Ww/VjCJb/ewl0n2XT4LF5uFu7r0/jiXsTdB4Z+a8yT2b8EFr2Z7+47ujcAYPaWY5xM1AVOKZlixf7jW2D2k8bX/Z6HBj1z79p/Opn7p6xj7cE4/DytTBjZET9PtxKtwTtPy1JJWu+UkBHn8qsFN000spSbpsH675y9omIzm01c1bI2v43pwbd3dqZT/epkZNmZsuoQfd9ZxNM/beLA6WRnL9NlDR/hIGqJjaDBGwh5YAFBgzcQtcTGsOHZAdKWATNGQ2os1G5j7AQgIuWjen3ch0wAYJRlLj99+7EOwKVUFBn7M1Jg+u2QkQhh3cns+x+e/mkzWXYHV7euw+XNazn3A7gYazFaltIzlZApKXerme7ZOyAt2nWyiEdfmMPhYFx2dczt3etTw9fj4l8suBlc85Hx9ZK3Yff83LtahQTQIawamVkOflgTcylLFhdUZOxPO2vEflsahF8JPY25MUfiU3n2581cMW4xUTtPYjGb+GhYexrVLOaMpDw8sxMyWXYHmVlKyEhl0rAXRL5ofD37KTi2ybnrKSGTyUSfpjWZcX83pt3TlR7hQdjsDqavPUzke4t49IcN7D6R6OxlupToaJg314R/5FZ8Wx7F6p+Gb8uj+EduY95ck1HG+PdLcHgNeATAzd+B20WU34rIRTM3H0RGt0cAeM72Kf+b9LuG/MolKVbsn/0UnNhq7PZ400QmLI9h+7EEqnm78fK1LZ39EVxOzuBktSyVvpy2pUudIzN/+wm2HknAx93Cfb0vsjomrzZDodNdxte/3APx55Ivo7KrZL5ffZDMC+2FLpJHkbE/2gG/jYHYfRAQSto1nzNr63FGTVxDr7ei+OGfGLLsDiKbBfP72B70iwi+qHV45Ukal6RtSZFNKoYej0LTAZCVbmQvUytf+brJZKJb4yC+v7srPz/QnX4RNbE74NeNR7ny/SU8MGUdW4+cdfYyXcLe7JEUnqGx+W73DDW2U0xaPRNWGbu9cMN4CGxYnssTkWzuV/yX1Lrd8DWlMebUK/zv13+0w4ZctKJif9qK72DjlOzZARPZk+bHh38bgwb+O7gFNf0u4cq/XBRzzi5LF/i1T89pWdK21yWSk5BZfyies6mZF/UaWfZz1TGjujcg0Me9dBY34A2o29443p8xytjxDBjYqg41fD04kZDOX9tOlM57SZVXVOy3LfsUdvyBw+zG363epvtHGxk7dQOLo09hd0CP8CB+fqAbE++4jJZ1Ay56HW4WM24WI6aVZLCvEjJSMZjNcP3nUC0M4g7AL/eB3V70YKYKqmP96nwzujOzHurJwFa1AZiz9TiDP17G6G/WsF7zEspU4+wLOGkxgfluT4sJolmNXbQ9cG52AM0GlfPqRCSXxYrXsG9J96xJhPkwHTe9zOSVBypt7BfnulDs71hnPS0P5swOeAF7/V488/NmMrLs9I2oyQ3tQ8p5tQIlrZBRQqYkQgO9aVzThyy7g+V7Tl/Ua/y28Qg7jyfi52nl3t6NSm9xVg8YOgk8q8GRdTD3WQAO7DPTOdDYAvtbDfeVYrpQ7O9dfxnNYv4LwETfe7h7gYPY5AzqBHgytl84i57sy/d3d6Vj/cB/v+xF8byInZaUkJGKwzsQbp4MVk/YPY/v7n37woOZKoFWIQF8fltH5j/Wm+vb1cVsgoW7TnHjZysY8dUqVu07o6vBZaBpU+g/wEFCVCuStoVgS/AkaVsIjmVh/HXnCMy2ZGOHr8tfcvZSRcSvFh7DviPLZOU6ywr2zxpHmytPV+rYL85RWOx3W1mbP0eNxGxPh4hB0PNxJi7fz7qDcfi4W3jthtaYTMXfSUNKT7GG+uZse62WpRLr09RovVi8q+RtS2mZWbz3l1Ed82DfcKp5l1J1TI7qDWDIV4AJ1k7kvZFTiIiACc/Ux2E3sWZ/LKt3XfpAYqn6Cov9vmsC+XXEHZgcWfxq78mrJ3vg5Wbh+UHNWPJ0P57sH0GDGj6lupactqWUDFuxn6Mx8lKx1G0HV4+D3x7ktpA3+XN4NZYHNCEtJpCoqFYMG25l7pzKd9DUpJYfH9zankeuaMpnC/cwc8MRlu85w/I9Z7isQXXGRjahd5MaOiAsRdOmmhg23Mq8We2yb3Gw9KGRhHrtBv8QuOkbsCgEilQI9btjvupVmPccz7t9z5ZbGrIquTVph2pU6tgv5e/fsd9symLNI0Oo5XEYAhvBDePZeyaFd+btAuC5Qc0JqeblxBW7Noup6KG+qpC5eH0iajJx+X4WR5/C4XCU6DhzyqqDHIlPpba/J6N7NCibBTa5Evo+B4te58GwJ5g11J3dNYLISvTAGpDG/W8fYsPXrcrmvaVK+XfsdzNnsOTRq6nudood9jCezbiLvhHBvHpdK0IDvctsHTk7LRmJ5OKdZyjVLBVOtM8Ixq8djdnk4Ivw/6NhwMHzh/JVUg1r+PDO0LYseqovt3UNw91i5p8DcYyauIbrP13O/O0nVDFTSqpXh7lzTERHw+zZcGrmh/QM/APMbsYQX9+azl6iiOSxO/ABpm27ETdTFp95fUhdvxNVJvZL+Tkv9v/4Gh0DFhpb7d4yBZubH09M30S6zU6vJjUY0SXM2Ut2aZbsM5ELtixlz5DxsOq0paS6NAzE083M8YQ01h4sfqlhQlomny7cA8BjVzYp02RYdJ2n+DP6Krzc0viu2fPU8D+FNcDYde+071G27Sh+64e4rn/H/pOTn6eF3xoSHN7cl/kY118WzsRRl5VpMgbytCxlFH8otSKbVDh798Ijc99iQ2YTqpmSmeA2Di/Scgcz7dnj5AWWgnrVvfnf9a1Z+kw/7uzREE83M5sOn+We79Yy8MOlzNp89ILlu1J8TZrAwCYLqLHpFeOGgW9BvU7OXZSInGfvPhP3/PYxO22hBJviGe/+Pu5k4hlqzD6oCrFfyk+TJjCw/m8EbnvPuOGaj6BWS75Yso+NMfH4eVh5a0gbVaY6mblYFTLa9vpiebpZuL6dMR/powXFz2pPWLyPuJRMwoN9GdKhXlktD4C9+8zcNnMCB7JqEWo+xUdun2AhC4cdLF6Z/LzmeJm+v1QtTZrAwNpTqBb9JQCPZj5Ip/YdeP2G1rktkmXJy73kLUtKyEiF07gxZGR5cPuO1zjl8Ke5OYZ33CbkDmoKD3fyAktRLX9P/ntNC5Y9E8mDfRvj62Fl5/FExk7dwFXvL+aX9Yexadu/SxO7D366Exx2aD8SOt1Z6EM1SFTEeRo3huRMX0bufIOzDm86mPfwsnUS9kyj5LcqxX4pBye2w8wHjK+7jYU2Q9l5PIEP/jZmYrx0bUvqZrcqKfY7j6VYM2SyW5a0y9JFGdMvHKvZxNLdp1l7ILbIx+8+kciXS/cB8HT/CKyWsj1dbNwY4tOqM3LnG6Q4POht2cLT1h/IPO0HwIazMUW8gkgeh9fhmPUYAOMyb8Kn9WDeualtgcmYsoj9OS1LGuorlVrOYKZd8yK5Y9drZDosDLas4p6kKPoPcNCkibNXWPpq+Hrw9IBmLHumH49e0QR/Tyt7TyXz+PRNRL63mGlrDpFhU2KmxNKT4IfbIC0eQjrB1e9BAVdDY2ONwaGVfYi0SGWWE/s3zRnAPXtexu4wMdy6kDuCf6fziANVMvZLGUmNgx+GQ2YyNOwDV7xCWmYWj0zbSGaWgyuaBzOkQ4hifwWQu8vSBSpk0nMrZHTacjFCA70Z2smocnk/OyFZmLTMLB6atoF0m53eTWtyZYtaZb6+nNi/eva1jN33HAD3Wf/kyugD4IANR89w6ExKma9DqoDEEzh+vA1TVgbzsjqxpPYoxt3cNjfO5CjL2J8z1DdNCRmp7KZNNRHZ28rsH2/n4dlvA/Ba71eZ8fqCfI+rale1qnm78+gVTVn+bCRPD4gg0MedQ7EpPPfLFvq8s5BvVxwo0S+4S3M44LcH4eQ28K0Ft0w2tlkswPARDqKW2AgavIGQBxYQNHgDUUtsDBuutjGR8pQT+2dMvY/nFxjbVL5snUT9sF9YtOtk7uOqWuyXUmTPgp/ugrj9EBCWO8D97bm72HUikRq+7rxxo9GqpNjvfDktS7asomfIqGXp4o3pF46bxcTyPWdYs7/wKpk35+xk53Hj9+TdoeXX0pcT+7+Z8hhvLDOqG77o9zTD6sUDMGOdUSWj2C+FsmXA9NsxJR5lj70uL5rG8MGwjrgVUOFVlrHfM3eXJSVkpJLLO5jp2lfu4mzj2zGbHPjNvRNO767yV7X8PN14sG84y57px4uDWxDs58Gxs2m89Ps2er29kC+X7CM5vfi9iS5p8duw/bdzQ3z96xb4sOhomDfXhH/kVnxbHsXqn6ZBoiJOkjf293n+MRLDbsDdlMVnbu/z2tS/WL0roUrHfikF8/8LexeA1Qtu/R58glgSfYqJy/cD8M5Nbanp56HYX0EUr0ImZ5clnbZcrHrVvRnaKRSA9+cXXCUTtfMEk1YcAIzfk2A/z/JaXr7Y3+7xF0mucwWellT+m/IqNTjLj2sO03+gXbFfCuZwwJ+PQ8wqEh1e3Jv5OE9f17nALa3LOvarZUmqnCZNYOAgEwHD3oXQrpB+Fqbewr23x7nEVS1vdyt39WzIkqf78er1rQip5sWpxHRem72Dnm9F8UnUbhLSMp29zIpn+2+w6HXj68HjIKxroQ/du9f41zM0/xWjqjREWqSyyYn9frd9ir1Wa2qYEvjQ8Tb3fLGEReuSqnzsl4u04XtY+Ynx9Q2fQ502xCZn8MSMTQCM7Fqffs2CAcX+iiJ3qG8xdllShcylyamSWbnvDB/8HZ1bce1wOJi79ThPTDd+T0b3aJD7e1LejNhvwef2ryGoCV6px/ja833ikxJZcei4Yr8UbPV42DCZLMyMzXyYFq07MqRDSIEPLevYn9uypAoZqXKsHnDLFAgIhdi93Ft9NNUjN7rMVS1PNwsju9Zn4ZN9eXtIGxoEeROXksm7f0XT480o3vtrF3HJGc5eZsVwbDPMvN/4ussD0OH2Cz68cWPj35yh0TnSYoIADRIVcSp3H8zDpmH3rkkL80He8vmA4GHLXSb2SwkcWgWzHjW+7vMMtLwBh8PB0z9t5lRiOuHBvjw/qHnuwxX7K4bcob4XOK/OGerroaG+lySkmhd39mgIwAd/7+aq95cwdfUhbpmwivunrCMuJZNWIf48O7CZk1cKeFWDYT+AZwBtieY169cE9Nmu2C/n27MA5j0PwOuZw9jp25nXbmhdaLtdWcd+T3e1LElV5lsTbp2KzezNVY0X8nrz9/Pd7QpXtdytZm6+LJS/H+/Dh7e2o0mwL4lpNj6O2kOPt6J4Y/YOTiWmO3uZzpN4InuQYwo06gdX/a/Ip+QMk0uIakXSthBsCZ4kbQshIapllR0iLVKpVAvFfOv3ZJncGWj5hyf8fsh3tyvEfilC3EH48TbIyoDm10KfZwH4ZvkB/t5xAneLmQ9vbZe7HSko9lcUOeMd7BfcZck4sfFQy9Ile3ZgMz68tR21/D04FJvC8zO3sGZ/LJ5uZh6KDOfHe7tVnMRXjXC46RvsmBlqXcL91X/Jd7div3AqGmaMBoedn+x9+DprEC9f05IAL7dCn1LWsd/bzdgZsiQtS9ZLe0uRclanDSd7fEHdpSO5y/tPDmTWZHLWVYBrXdWyWsxc1y6Ea9rUZd6243yycA/bjibwxZJ9TFpxgGGdw7ivTyPqBHg5e6nlJzMVfhgGZ2MgsDEMNQY5Fse0qSaGDbcyb1a73Nv6D3AwbWr5DLMTkSKEdeFUlw+ovepBHrHOZL+9Dr/aewKuFfulAGkJMO1WSD4FtVvDDePBbGbz4XjemLMDgP8Mbk7LugHnPVWx3/mK1bKUs8tSRUkUVGImk4nr2oVwRfNafLpwD1PXHKJfRDBP9Y/I3Qa+Qgm/nNMdXid4/bM8b53KQUct5ts7AYr9Li/5DEwdCuln2eXWgucT7ySyWS0GtKpd5FPLMvZ7uRuJY82QkSqt7uXX8k1Mzu4b39EzbbvLXtUym00MbF2HWQ/1ZOIdnWgXWo10m51JKw7Q++2FPPfLFtfYKtBuN9qUjqwDr+owYobxbzHlHSY3e7Yx8GvuHBPVi/8SIlLGag8YwY9HHwXgLbcJdDLtJOOkn0vGfsmWZYOfRsPJ7eBbG4b9CO4+JKRlMnbqBjKzHAxoWZuRXesX+HTFfucrzlDfNA31LXU+HlaeHtCMjf+9ivdvaVcxkzHZgq+5n1/ih2I2OfjQ7VOapRxx2eN+yWZLhx9HQNwBkrzrMSzxYcxuHrxybcti7QxWlrE/Z4ZMqlqWpKq7/p3H+evUcCwmO595fUjt1e5E9ra67FUtk8lEZLNazHywO9/f3YUuDQPJzHIwbc0h+r23iMenb2TPySRnL7PsLHwNtv9q7Kh0yxQIanxRL9OkCQwciP64i1RQV735Estir8HDZGOC+zjCa+2h/Q1HXDb2u7y5z8Kev40dlYb/AAEhOBwOnvt5C4diU6hX3Yu3bip6617FfuexFKNCJl1DfV2bycRlT33EElsbvE3pfO3xLh6Lg136uN+lORzw+0NwaCV2D39GpT5OLP48ekVTQgO9S/RSZRH7vdxL3rKkhIxUStUDTVz14YekBPfE3yORDU8OZe6Px13+qpbJZKJHeA1+vK8b0+/rRu+mNcmyO/hl/RGufH8xY6euZ+fxBGcvs3StnwxL3zW+vvYjaNDTuesRkTJTPdBMz3cnkBbYnkBTEt+4vU1G6CqWxxx19tKkvK38DP750vj6xglQtz0AE5cf4M8tx7CaTXw8rP0FZwmI850b6lucChklZFxVaIg3f7V6k2h7CCE+J9j36s3M/TXJ5Y/7XdLit2Dzj2CyMLHuK6xLrU1ELT/u6tnQ2SsDVCEjrsbqjvcdkyEoHLeUw9l9hInOXlWF0blhIN/d2ZnfxvTgiua1cDhg1uZjDPhgKfd8t5bNh+OdvcRLt+dv+OMR4+teT0C74c5dj4iUPXdvPEf/gCOgHo3Nx/jS7T2e/XENy/ecdvbKpLxs+zV3Vw2ueAVaXAvAmv2xvD7bmBvz4uAWtA/T2VpFl9uyVKwKGZ22uLLrujbnzsynOO0IwCNuC0y/HbIynb0sKU8bpsCiNwA42O1V/rejFgD/u6EVbpaKER80Q0Zcj3cgjPgJfGrCcQXngrQNrcZXozox++FeXN2mDiYTzN9+gms/Wc6oiWtYeyC2TN8/OhrmzKH0tyU8tgmmjwJHFrS5BSJfLOU3EJEKy682phE/4fDwp5M5mrfNn3L/d2vYcCjO2SuTbGUW+w+uhF/uBRxw2d3Qw0jKn0xIY8zU9WTZHVzXri63dyt4boxULOYiKmSy7A4ys/fE1lBf19apfnXcazRkdMZT2CxesDfKuCh3geoqKX9lFvv3/A2/PwyAvcfjPLCjDQA3dazHZQ0CL/TMcuWVs8uSKmTEpQQ2hOE/gpt3dnB+VMG5AC3q+vPp8A7Mf6wPN3YIwWI2sTj6FDeNX8mtE1ayYs9pHKX4c4uNhQEDHUREwKBBxjZzAwY6iCuN86X4Q/D9UMhIgoa94dpPoBhDvESkCglujunWqTgs7gyyrOFR+3fcMXFN1WvLrGTKNPaf3m3sppeVDhGDYODbYDKRYbMzduoGTiWmE1HLjzdubF2swY7ifDkzZOz2gu9Py3OVWS1Lrs1kMnFzp1C2OBrxhs/TYDLDxu9h0ZvOXppQxrH/2OZ8F2G/9RrJ9mMJBHi58dzAZqXwBqXHyz27ZUkVMuJyQjrCTd9kB+cpEPWqs1dUYYUH+zLu5nZEPdGHYZ1DcbOYWLUvluFfrWbI5ytYuPNkqSRmho9wELXERtDgDYQ8sICgwRuIWmJj2PBLfO3kMzD5Rkg6AcEtjSG+VvdLXq+IVEINe2G6/nMA7rLO4dbMmdz21RoOnE528sJcV5nF/oSjMPkGSI2DkE4w5GswGwe+r/yxjTUHYvHzsDJ+ZEe8s4cqSsWXO0OmkJalvAkZD6tOW1zdTR3r4WYx8fXJCA53/59x4+I34Z+vnbswKbvYH7sPpgzJvQh7st+7vDffKL95ekAEQb4epbD60qMZMuLaIgbA4A+Mr5e+B6s+d+pyKrr6QT68cWMbFj/Vj1Hd6uNuNbP+UDyjJ/3DNZ8sY+7W4xfs6b6Q6GiYN9eEf+RWfFsexeqfhm/Lo/hHbmPeXNPFlzGmJ8H3N8GZ3eBfz9je2jPgIl9MRKqE1jfBVcaB+XNu0+iXOo8RX63mSHyqkxfmesos9qfEGon4szEQFG5Uxbobu2lMXnmA71cfwmSCD4e1o2ENn9L7QFLmzKYLtyyl2YzSGXeLObe9SVxXDV8PBrWuA8BHZ3tC76eNO/58wpgtJU5RZrE/8YQR+5NPQq3WOG6ezAt/RJOUbqNtaDVuvSysVD9HafBWhYy4vI6jIPI/xtdzn4XNM5y7nkqgbjUvXrmuFcue7se9vRvh5WZh65EE7p+yjgEfLuG3jUcuuB1lQfbuNf71DM0/n8Yz9AwAe/ZcxEJtGfDjbXB0PXgFwsiZEBByES8kIlVO94egu9Fb/qbbVzRLWMbwL1dx/GyakxfmWsok9mekwLRb4dQO8KsDt/0CPjUAWLHnNC//sR2AZwY0I7JZrYteuzhHUUN9cypkPDTQV7KN7GrMh/pt41HOdnkKOt4BOOCXe2DfYqeuzVWVSexPOwvfD4G4/VC9Adz2M7/vSmb+9hO4WUy8eWPr3PhRkeS0VqZmZhW740DRTaqeXk9Cl/uNr3+9H6L/cu56Kolgf0+eH9Sc5c9GMrZfOH4eVqJPJPHIDxu5YtxiZqyNITOrkCbvf2nc2Pg3LSb/kK20mCAAwsNLuDh7Fsy8D/YtBDcfY5BzzaYlfBERqdKu/D9oNwILdj5z/5jasesY/uUqTiYqKVNeSj322zJgxiiIWW1UQ972M1Q3TsYOnE7mwewhvje0D+G+3o0udfniBDkboxRaIZOZs8OS5seIoWP96jSv40+6zc6M9Yfh6nHQ/BrIyoAfRsCRdc5eossp9difkQLThhsbtvgEw8iZnCSAl37fBsBDkU1oXsf/UpddJnJmyDgckG4r3nmTEjJS9ZhM0P8NaD0U7DaYPhL2L3H2qiqNQB93nuwfwbJnI3n8yqZU83Zj/+lknvppM33fWcSUVQdzt6AsTNOm0H+Ag4SoViRtC8GW4EnSthASolrSf4CDJk1KsCC73Ziqvu0XMLvBLd9BvY75HlJmE91FpPIwmeCaj6DpQDzI4BuPd/A7s4kRX67mdFK6s1fnEko19mfZjCveu/8CqxcM+xFqtQQgLjmD0ZP+IT4lkwZ+1bi7jYb4Vla5LUuFVsgYJzTa8lpymEym3CqZ71cfwo4ZbvwKGvSCjERj3siJbU5epWsp1dhvSzfO3Q4uAw9/uO0nHNUb8p+ZW4lPyaRFHX+uCGlcYY/7vfIkj4s7R0bRTaomsxmu/9zYhcGWBlNvhZh/nL2qSiXAy42HL2/C8mcieW5gM2r4unMkPpX//LqVPm8vYuKy/RcMNNOmmojsbeXMrHYc+fxyzsxqR2RvK9OmluCg2eEwWs82TjEGNt/0NYRfkXt3mU50F5HKx2KFoZOgYW+8SeM7j7exnNrOsAmqlCkvpRL77Xb4/SHY/itY3OHWKVC/G2BUTIyeuJb9p5OxnfVi6RsdadXCothfSRU11Dc9p0JGW15LHte1q4ufh5X9p5NZvvc0uHnCsGnGwO/UOPjuejh9MX0ycrFKJfZn2eDnu4wtrt28jVmRddry+6aj/LX9BFaziZRFbWjZ3Fxhj/stZhPu2QPI04o5R0YJGam6LG7GzkuN+kJmstGHeGyTs1dV6fh4WLmvT2OWPh3Jy9e0oLa/J8cT0vi/Wdvp9XYU4xfvJSnddt7zqleHuXNMREfD7NlGFcvcOSaqVy/mGzscsOD/YM0XxvfXfw4trsv3kDKb6C4ilZebJ9w6Dep1JoAkpnq8gf3ULm6dsIoTCUrKlLVSif1znoZNU8FkgZsm5ibi7XYHT87YxMYjcdjTraSf8qXO7csV+yuxoipkckr+1bIkefl4WBnSsR4A3608aNzo4Qe3/QS1WhtDYL+7DuIOOnGVruWSY789C34bAzv+yE7ET4WwrkSfSOS5X7YAUO1oOCv+8q7wx/05VTIpSsiIkH1gPhVCuxrDob67ztjLXkrMy93CHT0asvjpvrx+Q2vqVffidFIGb87ZSY83o/jw792cTck873lNmsDAgZSsXNHhgIWvwbJxxvdXj4O2t+Z7SJlNdBeRys/D17iyVrs1gZzlR4/X4PRubp2wimNntftSebjo2D/nGfjnS8AEN4w3ZkMADoeDN+bsYNbmYziyTKQfC8An/JRifyWXO9S3yBkyOmWR/G7rauyws2DHCfafTjZu9KpubPoQ1AQSDsO3gyH+kBNX6XouKvbbs4yqyM0/GIn4od9C434kpGVy/+R1pGRk0bZOEOu+C68Ux/05Oy2lKyEjks3dB0ZMz1PGeK0xJEouiofVwvAuYSx8si/vDm1Loxo+nE3N5P2/o+n5VhTvzNvJmUuZ1+BwwMLXYck7xvf934DL7jrvYWUy0V1Eqg6vajDyNwhuSQ3ime7xGpzZw9DxKzl4JtnZq5N/y2lRzamKvPZjaHNz7t3jF+/jy6X7ATgzpw1ugfn/P1Tsr5yKallKs2morxQsPNiPy5sFY3fA+EV7z93hWxNG/Q6BjYxkzKTBEB/jvIXKheXMitz4vZGMGfIVNBuE3e7giemb2Hc6mboBnoxo0B4c5kpx3O+VZ6el4lBCRlyDZwCM/AVCOhpJmW+VlLlUbhYzN3Wsx/zH+/DRsPZE1PIjMd3Gpwv30vOthfxv1nZOlrQ9wOGARW/AkrcBONXhdej2YIEPLfWJ7iJS9fgEGQfmwS2oQRzTPV/DGr+PoeNXEn0i0dmrkxwOB8x7HlaPB+BEl4+hw8jcu6etOcRbc3cCcG/n5iRvq6fYX0XktCzZHRS4RWzOUF8Pq05Z5HwP9jN+4X/ZcJij8XmqH/3rwqhZUL0hxB+ESVcrKVMR2e3wx0OwcQp2LBzr/iW0uhGAj6P2MH/7CdwtZj6/rSPtmnsAleO4/9zW19plSSQ/zwC47Reo2wFSY+Hba+DIemevqtKzmE1c27Yucx7pxYSRHWlTL4DUzCy+Wrafnm8v5MVft3IkvhgtAg4HqbNegcVvAfD4vNcIvm5MocO6SnWiu4hUXT414PbfoWZzajpi+dnzfwQk7eXmL1ayKSbe2asTu520X56EVZ8BcM8fH1J70O25sX/OlmO8MNO4gPJA38Y8f2Mjxf4qJKdCBoykzL/ltCx5qEJGCtCxfnW6NgokM8vBl0v35b8zIATu+PNcUuabQRC7r+AXkvKXZSN9+gOwYQpZdjPDf5pA3auGMGCgg4/m7eP9v6MBeOW6lrQNrVapjvtzWpa0y5JIQbyqGb2lOe1L314LB1de8stq22Uwm01c1bI2v43pwaTRl9GxfnUybHYmrzpIn7cX8sxPmwtvE7DbYc4zeK17H4AXYx5kevvmRQ7rKpWJ7iJS9fnWhFF/QHBLghxx/Oz5P0JSoxn+5SqW7j510S+r2H+Jsmzw2xg8t3yF3WHisYNPMqdLaG7sH3z/cR6atgG7A269LJSn+0cAiv1ViSXPduUFtS3lbnutXZakEGP7GWfi09Yc4vS/W+YDQuCOWRDYGM4eMpIyp3Zd8nsq9l8iWwb8NBqPnT9gs1u4/8ALLOtdnaDBG1idsJdxC3cA8PDlTRjWOSz3aZUl9ntlJ2TSMs/f9KQgSsiI6/GqBrf/CvV7QEYiTLkR9i68qJfStsvnM5lM9I0I5qf7uzH1ni50bxyEze7gx7Ux9Ht3EY/9uJE9J/O0CtizjHLF7LkBTx58jMk1exZrWNclT3QXEdfhW9M4MK/bAX9HAtM9Xycicwejv/mHXzccKdFLKfaXgqxM+OVu2DQVm93CmAPPMbNWh9zYX/3adRwOW4/N7uCatnV57YbWmLJP3hX7qw5znjORggb7aqivFKVHeBBt6wWQlmnnm+X7z39AQD0YPQeCW0DiMfhm4EVv8KHYXwoyU+HHEbDjd9Jt7oze9wrz6zbPjf0BvYyE2Yh24Tx2Rf6yl8oS+9WyJFIcHn4w4idoHAmZKTD1Ztj2a4lfRtsuF85kMtG9cQ2m3tOVnx/oRt+ImtgdMHPDEa58fwkPfr+O7YdOwIxRsGEKDszcPnM8P3j1yvc6xRnWdVET3UXE9XgHwu2/QVg3fBzJTPN8k55s4NEfN/LF4r0FzrAoiGL/JUpPgqm3wLaZ2E1u3DxjEn/4dMr3EM+wM5gsDjrUrMP7N7fN19qSQ7G/8rPmycgUWCGjob5SBJPJlDtL5rsVBwvc8RO/Wkb7Up22kHLGmClzYFmJ30ux/xKlxsPkG2H3X2SZvbj2h2ks9G9x3sPiV4TTw79pbhL+3yp67PfOrZBRy5LIhbl7w7AfjC01szJgxh2w5stiP13bLhdfx/qBTBrdmT/G9qR/y1o4HLB0yz4SvroOdvyB3ezOsZ7fMHnzsEoxrEtEKjFPf7jtZ2gciYcjja893uNG8xLemLOT//y6FVvWha9oKfZfouQzxm6HexeAmzdH+/zAzJ3Xnhf7TSZI2VWL1wa3w2rR4WpVlbdCJquAhGh6TsuSKmTkAq5sXit3c4lx8wtpSfIONFpXw7pBeoKRGNj+e7HfQ7H/EiUcM1rGDq0AD3+ORv7MX3uvIP24f76HpZ/w5+zSpjRpUrHakEoid5clzZARKQarh7HXfcfRgANmPwlRrxk7PhRB2y6XXOt6AXwxshPz72nKnIA36GreQaLDixFpT/HMwTr0GnKmUgzrEpFKzt0Hhv0IrW/G4shinPt47rP+wferD3Lnt2tJTCvgCms2xf5LEHcQJl4FR9aBV3W4/Xfq9b0id1BjWkz13D+/qXuDaZ/enuYROlStyvLOkLEXOEMmu0JGM2TkAsxmEy9dY1RaTF51kG1Hzxb8QM8AY5ZkxNWQlW5Uaa+dWKz3UOy/BKd3w9dXwclt4FsLRs+mXo/udB0Wg1eY8fN02CH1QBBnpnel/4CKW/1SHDkVfaqQESkuswUGvw99nzO+X/I2zLwfbOkXfJq2Xb5Ix7fS5LfrqZe+F5tXTb5s/DFraMXS3ac5FL6KxqP/IXlrCEc+j6yww7pEpAqwusMNX0C3sQA8Z53GG+6TWB59nJs+X0lMbEqBT1Psv0iH18JXl8OZPeBfD+78C0IvA4xBjR2uO45HSBwmEyRvq0u7pA788L1Owqu6vK1oBQ/1VcuSFE/38Bpc3aYOdge89Nu2wltQ3bzg5u+gwygjCzDrMZj/X2ODiQtQ7L9I+5fCV1cYQ5UDG8Ndf3HA2ogRX63mWNhmzJ420o8GcGR8JCd/7Foljvtzd1kq5gwZa1kuRqTSMJmg77NG1vbPJ2DzDxB/CG6ZAj5BuQ+LjjYy5OHh57ZdjopqBZjwDD1DWkxQnoqOgoNJ3teozNnfixL9F/w0GjKSICgc64gZPB7YiKGxKXy+eC8/rT1Mqm8ctW5ZQwO/atzZNZyRkcEU0kIqInJpzGbo/xr41YG//sMw83waeJ3i3hNjueaTZXw6vAM9wmso9l+qbTOzL3SkQa3WMPxHY/cTwOFwMH3zPo6H7cQE9KwTyn9Gt6ZZhAK/KzCZTJhMRmFyQS1LaWpZkhL4z9XNWbjzJGsPxvHL+iMM6Viv4AdarHDNh0bsX/wmLP/Q2BL7hgnGSINsiv2XaMMU+ONRsGdCSCfShn7PhHWJfLpwCek2Ox5WM49e0ZS+dRpyYJg5+2dU+WO/l1vJdllSQkYkr06joXp9mD7K6HH86nIY/iOxlgiGj3Awb+65INF/gIPPPzPxwINW5s1ql+/2gjK7sbEU+BrTpla86eClzuGA1V/AvOeMqxENesEtk42SdSA00JvXb2jNw5FN+GLJXqauPsSBxHj+O38t07b681BkOANa1sZcwFBHEZFL1n0sVG8Av9xDt8yNzPJ5ldtSHuX2r20EHW7GP1MaAkb8UewvAYcDlr4LUf8zvm/SH2762hisj1ER8eqs7UxacQCAu3s25IWrmxc6yFGqJovJhM3hKLBAIWeor4cqZKQY6gR48fDlTXhzzk7emLOTK1rUIsDLreAHm0zQ7zkIagy/jYEdf8DZQXDrVGJtdXXcfynsWRD1Kix73/i+5Y1ERbzMyxN2cCi7+rRneA1eu6EV9YN8AGge4azFlr6cba+LO0PG5CjulgKlKCEhgYCAAM6ePYu/v3/RTxApbyd3wtShRpWMuy+vbB3Pa78NwD9yK56hsaTFBJIQ1YrI3lbmzjEGee3Zc+Hs94CBxmT2wl6jyspMNcpBN00zvm8/Eq4eZ7QLFOJUYjpfLdvHlJUHSc4OZuHBvozp15hr2tSttAMeXTn2ufJnl0rk6EaYdiskHiPF7Md9aWNYam9DZrwXJrM9+2qoYn+xpCfCrw/CjuyhmV0fhKv+Z7QJY7SiPPrDRuZuOw4YV7bv7tXIWastU64c/4rz2Zv+Zw4ZNjvLn40kpJpXvvtunbCSVfti+WhYe65tW7c8liyVXIbNzsAPl7D3VDJXNK/FFyM7FrhLWz4HVxpbMaecAZ9gnvhnEh//2fmCx/1bd9k4YTnBsYw4jp5N4/jZNBLSMmkS7EurkAB+mhDAmrkB+PfZ4VqxPzUOfr4b9vwNQHKXx3js5CD+2nEKgNr+nrxwdXMGt6lTZZPv368+yAszt9KvkQ+T7utXZOxXQkYk23klhUmnjJ2XDhrb4r17bCSfVe+PPXv0UtK2EM7Makd0dNEliNHREBEBQYM34NvyaO7tJXmNSin+EPx4GxzbBCYLJ9v9H+vcxhDexFSszxuXnME3Kw7wzfL9JKYZZX/1g7x5sG9jbmhfD3dr5UrMuHLsc+XPLhXbebE/4agRt46sI8th5m3bzXyRdQ05FTKK/cVwZi/8MBxO7QSzGyc6vcN60+jcn/Hxs2ncO3ktmw+fxd1iZtwtbRncpuqebLty/CvOZ2/+4lxSM7NY+nQ/QgO98913/afL2RgTz4SRHbmqZe3yWLJUARsOxXHLhFVk2Ozc17sRzw1qft5jzov9sfuN2H9iK5lZVl44MobpwZ3JH/vb8n3UaVYeP8z87cdzW+oKY8+wYHY/VyVR5WP/iW3wwwiI24/d4sXP1V/mlZMNScqw4WYxcVfPRjwUGY6PR9Vu0vll/WEen76JLvW8mP7Q5UXG/sp1NiNSBmJjjSuYEREwaJDRIzpgoIO4zJpw+6/sr/0gAE/Wmcwkt7eogTG5vSRT1V1yMnv0PPiiDxzbhN0ziGe2/0Kt68cy6GrTuZ9x3IVforqPO49f2ZTlz0byVP8IAn3cOXgmhWd+3kK/dxcxeeWBYk8wFxHJq9DYn1UXRs8hpuZILCY7z7n9wAS3cQSQBIBXoxOAQ7G/MNtmwoS+cGondp/aPLblT2pfPTr3Z9xnSCyDP1rG5sNnqe7txnd3da7SyRgpWk71gob6SmlpH1add25qA8AXS/YxfW1M7n2Fxn5TQ7jrL44GDcHNYuPtsA/5wO1TfEgFwKvhSWqPWsbz89bwx6ajpGXaaRDkzb29G/Hq9a346vZOTL2nC/8d3IIutUKwJXrkS8ZAFY79Dgds+N4Y3hu3n2PpYVyx8wOeOhxKUoYNzxR/vh/Vk2cHNqvyyRg4N0MmvZjnKFX/JyJShOEjjHLyoMHnyhKjoloxbLiVqd+7cfvU16kf344J1z9Eb8sWZpuf49HMB/krpj9QvKnqeSez571KWiUns9syYMErsPIT4/s6bblj9mR++LsuQYM3nPczLk7Zpr+nG2P6hTO6RwOmrj7EF0v2cSQ+lRd/28ZHUXu4r3cjhncJw9tdIU1EiufCsd+D4T9+RMuU9nw46Bmusqyjhfl5Hs4Yy3qvptS4bgPBoa2AwlsvwcVif2YqzH0O1n1jfB/aldt+m8RPC2pkx/4z2BI9OVA7AVOyg2a1/fjy9k7nVUSI68npJrEVkJBJt+UM9VVCRkrmunYh7DuVzIcLdvPCzC3U9PWgX7PgImK/D7fM+IrOtva8deV/ud6ygramvYzNfJht3g2xeGfiabVwa+dQbmgfQpt6Aee13XRvXIOewdCsZRa1RizHo3Zi7n22RE+gisX+9MTsDVF+BOCfhN6MTrmbpFArDgdknPTj6IzO/He3O3PnOHmt5SR3hoy2vRYpWnQ0zJtrwj9yK74tj2L1T8O35VH8I7cxb66J629wsHqdjeknBtDlm7/ZkdqQYFM8U9ze4KnMmVw9ML1YJYc5k9kTolqRtC0EW4InSdtC8kxmL/vPWi5O74GJ/c8lY7rcz+7e85n8e/1Cf8a7dxf/5b3drdzdqxFLn+7H/13XkroBnpxKTOd/f+6g51sL+XThHhLTMsvms4lIlVG82J/FxJib6PHdHPalhVDPdJrp7v/HGPOv+Dc7zJjfl7Jiz+kLvo/LxP4T2+DLy7OTMSbo+TjRPWYx7Y86eX7G6XiGnMVkcZCyqxZvX9VdyRgBzlXI2AvcZSmnQkanLFJyj17RhMFt6pCZ5WD0pH947Ltt/PW3vcjY//G+kQxYPIkj9iAamk/wi/tLjGYuNU40ZMVzkbx8bUvahlYrdAZK06Zw1RVmzszoRtLO2tgzjf9+PUPi6Xh7NOHh5T4xpGwcWWdURG7+EUxm1td/jKGOB0mqZlwgNZnAo1Yi/v12lPiYvzLLqZBRQkakGIoqJ1+6xDhgrzVsFXvda9Nx3AomrBuF2eTgma4f8Ougy+H41mK917SpJiJ7Wzkzqx1HPr+cM7PaEdnbWuBk9krHbodV42F8Tzi6Hjyrwa1TYeBb7DngAZRuyb6nm4XbuzVg0VP9eGtIa+oHeRObnME783bR480oxs2PJj4l41I/lYhUUSWJ/dst9Wn3/iqmbrkJq8nOU+7T+d3rVbwT9zH8q9W8+OtWktIL39qyasf+LFg6zmhPPbkNfGrCyF/gipfYu9/Y2cSzfv6kVVaalVO/duTIQVU0ikEtS1JWTCYT7w5ty21dwwCYuf0AtUctw6vhqXyPy4n9K7cmU+PWFdQZtZw9Xa0MyniDvzI74WGy8ZLnd6zs8TSBGceK9d65sf+3jsSMG8DZlUbJ5Ok6u3l+5lbsBfz3XmnYMiDqNfjqSjizB/xDWNhtEkN2XQYedhy2/H/fqmyrViFyKmTSirnLkhIy4tLylpPnlVNODsYBu8XTRvDQf6g+ejXP2+/kpunfkmENxHp6i5EZXvIuZF24MqN6dZg7x0R0NMyebVyhnTunCmx9F7sfvrsW5j4DtlRo1BceWA7NrgaK/hlfStmmu9XMLZeFseDxPnxwSzvCg31JSLPx0YLd9Hgzijfn7OR0UvrFv4GIVEkljf1+o9bxcNpYbp85nkxLAC0d0cz1fIE7LXP4ftV++r+/hKW78x/g56iysf9UtFERueAVsGdCxCC4fzk0jgSgYSMHfpftw+KdPzmeurcWYKpaJftyScymCyVksluWrErIyMXxdLPwv+tb883oywj08sC9RhIW7/zH7CZrFvXGzifknsW410wip/AlNrUaw7e8zf2zxmEz++B2eCl83h3WfkOB+7TnkT/2m1jzVTNeva4lZhNMW3OI9/+OLquPXLaOb4GvLoclb4MjC1oN4beuP3LnQisOIHFTKMm78g/grpJtuhfgnZOQUYWMSNEuVE7es5dxYJD3gN0tMAXM8POO6zl87WrjANSeCVGvwhe94dCqIt+zSRMYOLAKTFe3ZRiJqM+6woGl4OYNg96Fkb9CQL3ch5VHyb7VYub69iH89WhvPh3egeZ1/EnOyGL84r30fCuKV/7YxvGzaZf+RiJSJVxc7DcxefMwDl+zAhr1w92Rzn/dJjPb6yWqn93GyK/X8OgPGziZWHCsqTKxPzMVov5nnJQc/gc8/OH6z42qSL9aAMTEpvDSolUERu7AZAZboge2RI+q2a4ll6ywliWHw0GaTS1LUjr6RQTz95O9qXY6DFuCZ777LN6ZWHwycNhN2BI9zt3uZQOHhS/W3cXhwcsgrBtkJMGsR+GbgXBie5Hvmzf2j+zWgDeHGMOGP47aw8/rDpfqZyxT6Ukw7wWjIvL4ZvAKhKGTmNHgFR794xAOB4zsWp9OtCIhqnXVbtMtQk5FX0oRu3DlUL2ouLxpU00MG25l3qx2ubf1H+DIvt1BVFQrwIRn6BnSYoJyg0qjNsHQeipsng7znoOT242rhR1uh8tfAp8aTvtMZW7/Upj9pLGlKUDD3jD4AwhqXODDL/QzLk1ms4mr29RhUOvaRO08yUdRe9gUE883yw/w/apDDO1Uj/v7NNbcAhG56NjfsF09aDsT1k2C+S/RLH0vv3v8l+9sVzJu4xAW7DjJ41c1ZWTX+lgtVewkcvffRuyP229836Q/XP0eVAsFwJZlZ9KKA4ybH01KRhZebhYC9jVn9dQwcraOLYvYL5VbYRUyGVl2cnI0HmpZklIQ6OPOwndaM2y4g79XpOIZFovZI5PWjT1552VvXnrSi8WLTPhHbjsv9jfo0Aja/QmrxxvtOjGr4Ite0G0M9H4KPPyKtYabO4Vy4HQyny3ay7O/bKZedS+6NAoq+onO4nDAzlkw51lIyE4gtbgOBr7Dn/vtPP3zehwOuL1bfV65tiXxfUwMG24q82P+iixnhkyGrXgJGZPDUcAErTKWkJBAQEBAkXtyi5Sn3buN3sbw8HNXMOPiYNhwB/PmngsiOUElX7l5SizMfxE2TDG+9/CHXk9Al/vBLX8WvlI7vQfm/xd2/Wl8710D+r8GbW6BQgab5VXQz7gsORwOlu05zcdRe1iz35gVYTWbuL59CGP6hdOwhk/ZLyIPV459rvzZpWK7pNifeALmPQ9bfwIgweTHuIwbmJJ1BQ2Cq/H8oGb0iwgudPBjpXFiG/z1H9gbZXzvVwcGvgXNr82N/RsOxfH8zK3sOJYAQOcGgbw7tC1hQd7lHvsrGleOf8X57L3fXsih2BR+fqAbHeufq0w7m5pJ21f+AmDX/wbgobYlKUWXFPvjY2Dus0aiAsAnGPo9D+1HgqXoege73cHYaeuZveU41bzd+GNsz4p5sfDoBqMq5uBy4/tqYTDoPWh6FRtj4rnli5Wk2+zc1jWMV69rle9vnSvH/dSMLJr/dy729BRiPri5yNivhIxIMRQ7qBxcAXOeMUr5AALCoO+zRsKiGAG6wko4agxuXPcN2G1gskDHOyDyP+AdWOTTK4LV+87wycI9LN1tDJg0m2Bwm7qM6RdORO3iXdW4VK4c+1z5s0vlVezYvzcK5j4Pp3YAcJA6vJsxhD/tXenSqCbPDmxG29Bq5bLmUhV3EJa8Axu/B4cdzG7Q5T7o8wx4Gr/HR+JTeW/eLmZuPILDAdW83XhuYDOGdgzFbK7kiahS4srxrzifvd+7i9h/Opnp93Wjc8NzxxQnE9Lo/PoCTCbY9/qgyp/YlEqj2LF/52z46wWI3Wd8H9zCSMxEXA3mC1dIpmZkceuElWw6fJb2YdWYfl833CpKVeXpPbD4Ldgy3fje6gndxhoXm929ORKfynWfLOd0UjpXNA/mi5GdclsPxUi4NXp+thIyIk5jtxvbvy34P0g8atxWvQH0ehLa3goWN6cur0TOHoZl78P67yArezBjk/5w1atQM8K5a7tIGw7F8enCPfy942Tubf1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      "text/plain": [
       "<Figure size 1400x500 with 3 Axes>"
      ]
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    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "def true_fun(X):\n",
    "    return np.cos(1.5 * np.pi * X)\n",
    "np.random.seed(0)\n",
    "\n",
    "n_samples = 30\n",
    "degrees = [1, 4, 15] # 多项式最高次\n",
    "\n",
    "X = np.sort(np.random.rand(n_samples)) \n",
    "y = true_fun(X) + np.random.randn(n_samples) * 0.1\n",
    "\n",
    "plt.figure(figsize=(14, 5))\n",
    "for i in range(len(degrees)):\n",
    "    ax = plt.subplot(1, len(degrees), i + 1)\n",
    "    plt.setp(ax, xticks=(), yticks=())\n",
    "\n",
    "    polynomial_features = PolynomialFeatures(degree=degrees[i],\n",
    "                                             include_bias=False)\n",
    "    linear_regression = LinearRegression()\n",
    "    pipeline = Pipeline([(\"polynomial_features\", polynomial_features),\n",
    "                         (\"linear_regression\", linear_regression)]) # 使用pipline串联模型\n",
    "    pipeline.fit(X[:, np.newaxis], y)\n",
    "\n",
    "    # 使用交叉验证\n",
    "    scores = cross_val_score(pipeline, X[:, np.newaxis], y,\n",
    "                             scoring=\"neg_mean_squared_error\", cv=10)\n",
    "    X_test = np.linspace(0, 1, 100)\n",
    "    plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n",
    "    plt.plot(X_test, true_fun(X_test), label=\"True function\")\n",
    "    plt.scatter(X, y, edgecolor='b', s=20, label=\"Samples\")\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"y\")\n",
    "    plt.xlim((0, 1))\n",
    "    plt.ylim((-2, 2))\n",
    "    plt.legend(loc=\"best\")\n",
    "    plt.title(\"Degree {}\\nMSE = {:.2e}(+/- {:.2e})\".format(\n",
    "        degrees[i], -scores.mean(), scores.std()))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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